On the existence and objectivity of Abstract Entities

The thing is by definition minds wonder and enquire about, their nature is relational, a property that requires differentiation to produce any outcome...this differentiation does not need to imply a fundamental dualism between body and mind, once mind or consciousness or awareness do not necessarily imply any sort of free will...but instead the implication could well be that the very concept of mind can be reduced to the notion of body in which process between parts is all there is...

In other words Fil, nothing is entirely anything while everything is partly something else

...the fact that things relate doesn't mean that they don't are things but only that whatever they are is useless without a context...a subtle yet important difference...

.Dear Friends,
I followed the discussion started by my post and and the replays to it of dalehileman and fresco . I see that thread as a collective effort to help answer some questions related to the definition of the concept of “existence” of abstracta and , and to the objectivity of this special case of existence.
Problem is, with each new replay in the thread, the discussion went farther and farther from the target of the initial effort ,in the end the discussion getting at the level of abstractness absolute necessary to get a sophisticated ,esoteric non-answer to anything to be answered , but brilliantly answering any question not asked . And, wonderful in the philosophical discussion, anything goes ! For example , the abstracta existence getting a subjective nature , even if most people in the field consider it as objective (numbers, for instance) . Perhaps this is what made necessary ,at its time, the Socrates dialectic method , and produced later , the Cartesian need for “distinct and clear ideas” in order for God to conduce us to epistemological truths !
As well known , the “exact” sciences have their roots in the philosophical thinking and their success is partly due both to the approach based on Descartes principles of clarity in thinking (and from here, in formulations) and , to the use of clear definition of the concepts utilized .
No undefined concept can be used to understand or ,at least, to get an acceptable idea, of what goes on in the Universe. From the same reasons ,in scientific abstract formulations people are trying , when the case, to maintain a clear relation to the primary, brut ideas. This helps in turn, to have in mind , again, ”clear and distinct ideas “ , a good principle , apparently not always respected , I’m afraid, in our philosophical discussions.
In the last years, the philosophy of mind ,in which I’m interested , shows more and more, a tendency to become an interdisciplinary science ,making use, beside the philosophy, of ideas and results from sciences like psychology , neurology ,linguistic etc. (The cognitive science is one product of such an interdisciplinary effort.) It is with this situation in mind , that I try to discuss in order to better understand , some basic concepts ,as the abstracta existence and, the objectivity of this existence . The controversial position of Nominalism as opposed to the Realism in what concerns the mind states ,all abstract, motivates such a philosophical discussion.
Now, it is possible that I failed to see that my questions have been indeed answered even if in a language appearing cryptic to me. In which case , I have to apologize !
It is also possible that my initial post was by itself badly formulated. Reason for which, I’ll post here a new version , hopefully better than the first .Hopefully…..

In a precedent post (Definition and objectivity of abstracta existence, 6.7.12), I formulated some questions related to the need for a definition of the existence of abstract entities . In this post I reformulate some points, hopping to make them more clear ,at least to myself ! Also, I introduce here the concept of model , in the context of what I hope to be a starting discussion, on the objectivity of abstracta existence .As said in my previous post, due to my professional formation, I try to reach philosophy from a scientific standpoint , using where needed and if possible , the thinking methodology long time accepted by the scientific community .
A definition of a certain category of objects, doesn’t create objects in that category ,but can create a working device, for the recognition of a particular object as belonging to the defined category. When possible ,the definition has to be intensional, able to provide a necessary and sufficient condition for such a recognition..
With the human collective experience , gathered from the beginnings , a definition of concrete things based on human sensorial capabilities , is accepted also as a definition of their existence . A concrete thing exists iff. , its features satisfy the definition of concreteness: it can be seen, touched , it is there and only there (non-ubiquitous) , etc.
For us humans, the existence of a concrete thing results just from it satisfying the definition of concreteness !
The abstractum is complementary defined, as any non-concrete entity ,but in contrast to what happens in the case of the concreteness concept, this definition, while allowing us to recognize the abstractness , does not provide also a necessary and sufficient condition of existence for abstract entities. Just by being abstract ,just by satisfying the condition of abstractness, a certain entity cannot be described as existing in the same sense as a concretum! Thus, in order to be able to ascertain that a certain abstract object exists, a definition of the concept of existence of abstracta has to be found . Not just of the existence , but of the existence of abstracta . The use of the same word “existence” for both categories of entities, without any qualifier , is deceptive ! I don’t know of any definition for the abstracta existence but, if somebody here can put forward one, this would be highly appreciated ! To insist more on this point ,we see that the two category of objects , concreta and abstracta , form a dichotomy , more specifically a bipartition. Indeed, the two categories are jointly exhaustive , any object in the Universe has to belong either to concreta OR to the abstracta category and, mutually exclusive, no object can be at the same time both concrete and abstract . The objects of our universe are all part of one or another of these two totally different partitions of the Universe . How then, can we possible use the same existence concept, for both ? ( It is not here a matter of finding a synonym , but a different concept ! )
In the same context, it seems to me appropriate to introduce here a concept widely used in science and technology , the concept of model . To put it simply, when trying to understand , starting from empirical observations ,a phenomenon or a process , be it natural or artificially produced , we put together , in what is called a model of the analyzed process, a set of hypothesis which could possible explain the empiricalobservations . If such a model can account for the observed facts or data ,then it could constitutes a possible step forward, toward a theory of the process we try to explain . Examples of such models are the “water as first principle” in Thales cosmogony , the geocentric system of Ptolemy , the dependence of the speed of falling corps on their weight, as thought by Aristotle , all wrong models ! But also, the heliocentric system of Copernicus , the Newton mechanics , the special and general relativity of Einstein, the quantum theory, the role of chlorophyll pigments in assimilation , the atomic model of Bohr etc. Some of the models In the last examples, have survived the onslaught of experimental “tests” and became thus ,theories . The gravitational field , as well all the other “fields” , are considered by many physicist just models , expecting to be confirmed (or not !) , as a true theory .
I introduced here this concept ,the model , because I intend to put to discussion an epistemological problem: the possibility that we humans, in our effort to make sense of the Universe we are living in or, of the Nature we are part of, try to formulate our empirical observations, in our terms. To this aim ,we artificially divide the Universe we know in more or less independent sub-universes ,call these sub-systems, and build for each , a model. model . ( In what measure such a model correctly represents the modeled sub-system, the nature itself, is a much more difficult epistemological problem than I’m willing or able to discuss .But, If somebody can do this competently, I’ll be grateful !). I have to make the mention that even if the results we obtain using the model are reproducing the empirical facts or numerical data , this doesn’t mean the model tell us about the nature itself ( The Ptolemy model is a case in point !) .
Let us suppose we adopt the above position . We could than speculate that most of the abstract objects are in fact produced as a result of human propensity to identify, compare, classify and label anything we are aware of . And, In this endeavor , we use not the Universe itself but , our models of its subsystems ,all abstract ,all, in a more general sense “invented” by us and thus, part of consciousness . Such a position, if correct, could open a new perspective on what has to be meant by the existence of abstracta ! If, for instance, we imagine our circulatory system as being activated by a pump effectuating N cycles/min ,than ,in this model of heart, its debit is described by the equation
D= R*N*V
where R is the “ejection fraction” , the fraction of the heart volume V ejected at eachoftheN contractions/mim If four numbers D,R,N,V can be found, (in a naturally acceptable range) , which satisfy the equation above, then we can celebrate ! We got a heart model : “we know” now that the heart is a pump ! As abstract entities, the four number D,R,N,V exist just exist because they satisfy the heart model equations. Both the heart model, clear a product of our mind, and the foursome D,R,N,V , are abstract entities .It seems to me that both exist just in our mind and, will disappear with it ! Thus to me, they are subjective abstract objects ! The relational operator “=” is by itself part of this model, it is an abstractum with the same subjective existence as the other elements of the model !
As we see , such a epistemological position , while giving a possible definition of abstracta existence, seems to put the largely accepted objective existence of abstracta in jeopardy!
WHAT A SHAME ! but
Honi soit qui mal y pense !

...2 or 3 remarks...
...regularity's exist in nature not particularly in mind...mind may or may not, recognize the existence of those patterns...abstract objects are just regularity's in nature as its objective existence is dependent on whatever exists in nature...the very substantial qualification of abstract makes no sense without a qualification for the concrete objects of our phenomenal experience...finally to make notice that the very idea of mind is part of our phenomenal experience, a natural one...