Napoleon Bonaparte – Jacques-Louis David 1805.
What are numbers, sets, groups, points, etc.? Are they real objects or are they simply relationships that necessarily exist in all structures?
The first point at issue is the interactivity and so of relativity of reproductivity and the dynamics of integrity, autonomy and independence.
In reality, in existentialism and in evolutionary cosmology, human beings and by extension human mind are integral parts in the energy driven evolutionary dimension of energy and of interactive mass of the universe of nature and the planet. All inorganic, organic, biological and human, including technical entities are interactive (and reproductive), therefore relational, organisational, conditional and evolutionary. Both integrity and independence of entities are interactive, therefore relative and variable. There is no absolute independence in the Universe. This is the fundamental point which the reader has to understand before going any further.
More specifically energy, interaction, reproduction, biology, organisms, human beings, human mentality and intelligence and everything else, are integral parts in the energy driven interactive and evolutionary context of the universe and the planet. The features and properties apply universally and uniformly and human beings are interactive parts (parts) of the energy context, not independent creatures. Human beings are in fact the highest interactive and reproductive motion controlling, evolutionary creatures known. So it is natural and sensible that the autonomy, liberty, mentality, intelligence, accentuation of human logic and psychology in the human information management and in the control of motion is the highest, known. Human dependence and independence on the environment and on universal condition is likewise highly dynamic, interactive, reproductive and negotiable and so is our integrity and independence. We are still and nevertheless always interactive, integral evolutionary creatures so our independence and integrity, no matter complex, simple or variable, is still dynamic and negotiable, relative, real and material, interactive and reproductive.
This evolutionary origin and universal relation (interaction and reproduction, integration and composition) and direct recourse to the fundamentals, rather than divine intelligence (ever present and integral in energy dynamics), explains the awesome, human simplicity and facility in the conception and comprehension of the energy fundamentals. Across universal, natural and human (technical) evolution and specifically through philosophy, science, academic discipline and the works of life, from theoretical physics, biology and neurology, through to history, civilisation, business, arts, sports and athletics.
Put simply, relations exist in all structures. This meaning energy relations (interactions) andorganisations (reproductions). These relations are variable between low (dynamic) definition (massive, quantum, potential and intangible) and high (dynamic) definition (material, physical, real and intangible). So we also exist, as interactive human beings. So does exist our mental perception of relations, mathematical or other, real or potential.
The existence of reality and potentiality is distinct in the variations of definition in space-time dimension (and information) and more specifically in the interchange of quantum (energy and quantum) and physical (material and physical) states.
Truth is corrolary of interaction and especially of reproduction (information and record).
The second point at issue is intelligence and by extension, the (interactive and reproductive) mental functions of perception, interpretation, conception, comprehension, cognition and consciousness.
As mentioned, all energy structures, inorganic entities and natural creatures are evolutionary. The intelligence variation between any of them and the human beings (homo sapiens sapiens), is always dynamic, only biological and neurological, interactive and reproductive and only regarding the control of motion and specifically that which evolved from the control of the 3-dimensional motion, in the human case, of the free hands. Corresponding to the control of motion, is the control of interaction (relational) and reproduction (organisational) and jointly, conditional, economic, technological and ecological.
Intelligence is the (interactive and reproductive, biological and neurological) mental (rational / physical and emotional / quantum) management of this information (dimension etc.). The assessment is relative and contextual, real (for the past) and potential (for the future) experienced and conceived, in the current (running) present.
For example the intelligence between a mathematical equation, a relativistic jet, a turtle, an artwork, a neurological function and an astronaut, is qualitative (interactive) and quantitative (reproductive). Above this, it is relative and contextual (dimensional, organisational and conditional) and above all, dynamic. So is the standard of human intelligence.
Put simply, human intelligence is what we do next. Mathematics is the mental function that facilitates calculations for the human control of motion. Same with the control of motion, is the control of interaction (relational) and reproduction (organisational). Same with instrumentation and technology etc. So the human understanding of mathematical relations is real, relative, integral, universal and evolutionary. Plus in human neurology the control of motion is mental,
- Reflexive, therefore emotional, fast, approximate, probable (quantum) and less structured and reflective, therefore logical, slow, precise, approximate (quantum) and less structured
- Reflective, therefore logical, slow, accurate, programmed (physical) and more structured.
So intelligence is the neurological, sensory – motor combination (interchange) of the two, in the biological, metabolic and mental, sequence of interchanging (relational) interactions and (organisational) reproductions.
So intelligence is the neurological, sensory – motor combination (interchange) of the two, in the biological, metabolic and mental, sequence of interchanging (relational) interactions and (organisational) reproductions. Energy exists in reality, potentiality and materiality. So do its dynamic properties, like limitation, variation, dimension, mass, motion and information. So, do derivative attributes, like structure and form, system and function. Finally, so do energy dynamics developing, dimensional interchanges and physical,
- Interactions, which are relations
- Replications and reproductions, which are organisations
- Both, which develop conditions.
Energy and the universe are dynamic and dimensional, therefore kinetic and evolutionary.
Material mass is not static. So is further not,
- In physics, in motion and information
- In biology, in metabolic and reproductive interactions
- In neurology, in mentality and intelligence
In standard academia, the conception of the relevance and materiality of motion and dimension and of time and information, is elementary and fundamental. So is in every theoretical or applied discipline, including in relational and behavioral psychology, in organizational economics or in conditional sociology.
For this reason, dynamic energy is in fact more real than material mass. As mentioned definition is variable, relational, organisational and conditional.
In metaphysics, true is that (motor reaction) which produces (d) an effect (sensory action) and that (interaction), which if repeated (replicated), will produce again (reproduce), that effect. In this sense therefore, true is that which repeats (replicates) itself.
In epistemology (theory of knowledge), right is that (motor reaction) which produces a pre-meditated (intended and/or desired) effect (sensory action) and that (interaction) which if repeated (replicated), will produce again (reproduce), that pre-meditated (intended and/or desired) effect. In this sense therefore right is that which is useful, effective and consequently successful.
In ethics, good is that (motor reaction) which produces an effect (sensory action) which is positive and beneficial and that (interaction) which if repeated (replicated), will produce again (reproduce), that positive and beneficial effect. In this sense therefore good is that which is favorable and helpful.
In aesthetics, beautiful is that (motor reaction) which produces an effect (sensory action) which is pleasing and attractive and that (interaction) which if repeated (replicated), will produce again (reproduce), that pleasing and attractive effect. In this sense therefore beautiful is that which is satisfactory and appealing.
In existential ontology and in theory of mind, real is the relational and more over the dynamic. Definition is matter of quantum mechanics and classical physics, configured into modern mathematics.
Logic, deals with quantum state of information, therefore is rational and reflective, mental function (thinking).
Psychology, deals with quantum state of information, therefore it is emotional and reflexive, mental function (feeling).
Numbers, sets, groups, points, etc. are mathematical (geometrical etc) configurations of energy variations and so relations.
So numbers, sets, groups, points etc., exist in the terms, described. Yet the real is not fixed or static. Real (and material) is the variable, dynamic and kinetic, in essence and interpretation and in conception, comprehension, information and communication. Truth is determined by the interchange of reality (physical) with potentiality (quantum), in the dimension of the energy developed, material mass.
Therefore formal constructions and mathematical relations are variable and dynamic, fixed and floating (fluctuating), interchanging in quantum wave – particle dualities and in other dimensional states of energy and conditions of motion, according to velocity, acceleration and momentum.
Singularity is real because of the Plurality potential. 1 is real, because of its potential variation in 1+1 = 2. And so on and so forth, repetition and replication of 1+1 and 1+1+1, will always produce 2,3 etc.
This motion of the past to the future in the current (running) present and so the flow of the definition of probability to program, defines reality. Put simply, one is real not because it is static in absolute singularity but because it is dynamic and potential to become many in relative plurality and multiplicity. And the reverse in interchange. A scale of the dynamics of energy and the measure of material mass, provides motion in the present, with its power to fix the future and which its force to flux the past.
This much about the partitions of philosophical scholarship into the two opposing schools of thought: platonism, which asserts that mathematical objects are real, and formalism, which asserts that mathematical objects are merely formal constructions.
In this virtual but not longer real, opposition conondrum, this column, may settle for interchange.
P.S. Notes
Regarding the “continuum hypothesis”, and the claim of propositions which can neither be proven true nor proven false, the formalist answer on context is clearly provided above and specifically in the dynamics of relativity and approximation. On the same hypothesis, the platonist assertion that either does or does not exist a transfinite set with a cardinality less than the continuum but greater than any countable set, applies the same, for the economy of repetition and the fidelity of replication.
