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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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RKS"Why not start an IDM thread to discuss IDM specifically? As I recall, you’ve had your own Yahoo! forum from time to time. Yet you follow me around…>/i>
WHAT!? I HAVE BEEN ON THIS NATURE LIST WAY BEFORE YOU DUDE – ALMOST FROM THE BEGINNING (invited by Samer) – you only started posting recently so dont give me the above rubbish. As for IDM I DO have a list for it and continue with it but I am allowed to discuss things on other lists such as meaning derivation on a list focused on mind and brain – and have been for years. Your sudden attacks on me make me highly distrusting of your motives for such since all I have seen so far is rhetoric, no counter evidence against the model.
As I have said here and in response to your recent (this morning) attack on your own list, THERE IS NO INFINITE REGRESS PROBLEM. The fact you ignore the prose covering the organic from the mechanistic means that despite moderating the posts you have chosen to ignore that fact for your own personal reasons – that is not good science dude. If your model is not up to scratch it is not my problem that mine can do better; you need to lift, not try and rubbish models that work and are in practical use.
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Chris,
You say that you do mention eight basic categories and list them. I was referring to the categories mentioned in the message I was responding to, vis:“What IS present at this pre labels level is recursion and the emergence through mechanical means of categories usable to represent experiences as ‘wholeness, partness’ etc. The recursion has a property where at a specific level in development there is a transition from a mechanical dynamic (and so infinite regress issue) to an organic dynamic (a brake system where the categories derived pre this level become usable not just literally but also figuratively. This forms a brake in deriving meanings in that the one set of meanings is now applicable to MANY contexts – we transcend the single context position).”
AND
“GIVEN the recursive nature of language development so the base level pre labels covers recursion of the differentiate/integrate dichotomy and gives us a dimension of vague categories usable to set a ground for all emerging subjective perspectives and that includes the properties and methods of “Consciousness”.
Due to the recursion and closed system of categories so we move from the general to the particular and in doing so discover that all categories are in fact reflected in EACH category in the form of being usable as sources of analogy to describe all of the properties/methods of any class. This ‘entanglement’ being a property of recursion.
The identified methodology in meaning derivation is applicable at all levels such that a focus on each category allows for extraction of details through analogy to all categories – ad infinitum if you like – this being a property of language."
So, when you use categories as above you are referring to
OBJECTS:
111 – Mediation of wholeness through differentiation
000 – Mediation of wholeness through integration
101 – Mediation of partness through differentiation
010 – Mediation of partness through integrationRELATIONSHIPS:
110 – Mediation of static relationships through differentiation
001 – Mediation of static relationships through integration
100 – Mediation of dynamic relationships through differentiation
011 – Mediation of dynamic relationships through integrationThe above are “a closed system of categories” and “all categories are in fact reflected in EACH category”. Thus all of the above categories except of 000 is reflected in 000???
If not, give examples of the categories that you actually were referring to.
Robert
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RKS:
“So, when you use categories as above you are referring to
OBJECTS:
111 – Mediation of wholeness through differentiation
000 – Mediation of wholeness through integration
101 – Mediation of partness through differentiation
010 – Mediation of partness through integrationRELATIONSHIPS:
110 – Mediation of static relationships through differentiation
001 – Mediation of static relationships through integration
100 – Mediation of dynamic relationships through differentiation
011 – Mediation of dynamic relationships through integrationThe above are “a closed system of categories” and “all categories are in fact reflected in EACH category”. Thus all of the above categories except of 000 is reflected in 000???
If not, give examples of the categories that you actually were referring to.
Robert"
The bit domain allows for representing ANY form of dichotomy and for representating any INTERPRETATION of that form – ie as symmetric, anti-symmetric, or asymmetric.
In the particular focus on categories of meaning the ASYMMETRIC interpretation is of interest in that it covers aspects/whole dynamics. Thus mapped to the 1/0 dichotomy so the set of POTENTIALS within a whole are represented in 000 (or 000000 etc where it is this six-bit level that gets interesting). The asymmetry of the interpretation means that the sequence of bits moves general to particular. Another form of interpretation is to waves, each bit reflects a specific frequency 1/2 that of the previous frequency and the whole sequence sums to a unique waveform.
As 0 = potentials so 1 = actuals (as a PULSE interpretation 1 is positive, 0 is neutral, as a WAVE interpretation so we have a sine-wave format). In the neuron the raw data sums to comes in as a wave form, AM bias. It gets digitised into a PULSE form (FM) for output (also interpretable as a spectrum – the WHOLE sensation is cut up into a properties/methods list, general to particular. This means the general gets laid down first and small difference come later – very energy conserving).
Mediation through integrating covers the use of potentials, drawing-in to map an IMPLICIT wholeness. As 0 covers potentials it covers negations (NOT actuals) and contributes in mapping potentials, possibilities.
When we get to the six-bit patterns we find, when we focus on specialist interpretations such as yang/yin or fight/flight etc, a QUALITATIVE change in that the literal forms of categories can be mapped to presenting descriptions of all of the other categories, more so their PARTS, by analogy. The closed system of the recursion elicits a GROUP theory aspect that presents A o B is described by C where A, B, and C are elements of the set of categories.
The base level in the neural hierarchy allows for emergence of different classes of meanings but all applicable within the ONE context and as such no labels required. Thus the specialist dichotomies such as 1/0 or differentiating/integrating or positive-feedback/negative-feedback or what/where or male/female or light/dark or far-from-equilibrium/equilibrium or femions/bosons or RNA/DNA etc etc etc, all interpreted as asymmetric, reduce to a SINGLE set of patterns present in that base level and so at that level ‘equivalent’ in general.
Given this equivalence I can use the BIT dichotomy to form a BIT domain through recursion and that domain can be used to map out properties and methods present in all of the other domains and that includes the differentiating/integrating domain aka what/where domain where such is the main source of activity in our neurology – mainfest in the brain oscillations across such dichotomies.
The basic domains are identified in the IDM Abstract Domain model page linked to the below signature.
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To flesh this out:
“When we get to the six-bit patterns we find, when we focus on specialist interpretations such as yang/yin or fight/flight etc, a QUALITATIVE change in that the literal forms of categories can be mapped to presenting descriptions of all of the other categories, more so their PARTS, by analogy. The closed system of the recursion elicits a GROUP theory aspect that presents A o B is described by C where A, B, and C are elements of the set of categories.
The base level in the neural hierarchy allows for emergence of different classes of meanings but all applicable within the ONE context and as such no labels required. Thus the specialist dichotomies such as 1/0 or differentiating/integrating or positive-feedback/negative-feedback or what/where or male/female or light/dark or far-from-equilibrium/equilibrium or femions/bosons or RNA/DNA etc etc etc, all interpreted as asymmetric, reduce to a SINGLE set of patterns present in that base level and so at that level ‘equivalent’ in general."
The qualitative change is in the form of self-referencing the self-referenced. For example, given the category of 101110 if we apply recursion in the form of stepping through the sequence and ‘flipping’ the bits in a binary order we get all of the other categories and cognitive analysis shows that they are used to inform of the nature of the original category – its properties and methods, through the use of analogy.
As such the ‘genotype’ is represented in the core set of categories derived from self-referencing. The ‘phenotype’ is represented in the derived set of analogies from applying self-referencing to the original category (and so self-referencing the self-referenced). As such each category has a genotypal form and a phenotypal form where the latter is dependent on the context in which the genotype is expressed. If expressed in its own context then it is literal, in other contexts it becomes figurative. This is akin to music where a note (a category) can serve as the KEY as well as be involved in the make-up of the melody/harmony expressed in that key.
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