What is the vector field? The space of possible implantations by concepts? This definition may have some value and as this is a fairly ad hoc piece of writing we’ll leave it for now. The concept of the vector field as explored elsewhere on the blog seems, in a sense, so boringly familiar. It’s the idea of uninterpreted existence. Any region in any plane that it is possible for us to name is part of the vector field. Vectors as individuated regions given names are commonly called objects except this is in a sense one stage further than vector because object is still a concept. The rejoinder to this is that of course a vector is also a concept. Yes and this is the reason the term vector field is employed, this at least gives the prior heuristic of undifferentiated stuff. This undifferentiation though is not a description of a spatio-temporal surround of the organism, rather it applies to every plane. So the mind and the contents therein are also part of the vector field. Questions as to whether or not the notion is helpful in understanding a thorough description are precisely the point of the writing.
The vector field is broken up into regions, as mentioned these are the ‘objects’ or ‘vectors’. The term vector is there to emphasise the way in which the region is capable of taking a usage word within it -the vector is host to the concept. Any region of the vector field that can have the word cup employed of it is potentially a cup (that’s the grammar of saying ‘this vector houses the cup concept’. Regions that cannot take this usage are not cups. A key question that arises that any such theory must face is ‘what is doing the breaking up into regions?’ This is answered in the same way. Vector theory in a sense is a phenomenology. It cannot tell you what the subject is because ‘subject’ is a concept imposed upon a region of the vector field. Vector theory cannot privilege one term for the mind, individual, subject, dasein. Philosophical argument ensues when a) one says that this vector is best suited to this concept and others disagree and b) there are no clear criteria that can be established to enable a relatively settled fixation of the concept-rules. Consciousness is a perfect example in this way. No clearly agreed boundaries or nature exist for the application of the rules for this word. In this way the notion is related to manifestationism which can itself be subjected to vector theory. In manifestationism ontologies are the implantations for the vector field itself (what is the nature of everything?) We then argue philosophically about which is the most logically cogent ontology. This in turn raises more fascinating challenges for vector theory.
Do formal systems plug into vectors? Surely they must, but non-physical ones. This goes too far already since physical is a concept applied to the vector field. Numbers are relatively easy (maybe). The possibility of number needs the concept of individuation to facilitate it. There must be in the vector field the ability to group separate regions of the vector field to form the rules ‘this is two, this is three’ -note this does side with transcendental realism or idealism, these are manifestations that are possible interpretations of the vector field.
But what about logic? Logic as an expression is applied to the field on a level in which the concepts are considered related to each other in a certain way. There are rules for the language game of ‘that sounds logical’ but formality takes it to another level. Logic formally uses a variety of concepts but again (and this is what we have to mean by a variety of planes of the vector field) ‘and’ is a concept applied the notion of grouping vector field regions just as ‘or’ is a concept applied to a minimum of one alternative obtaining out of a minimum of two choices. I think this must related to accretive nature of pneuma (information). Conceptuality must be functional in some sense for logic to be possible. Concepts act as a vectors for the possibility of logic. The extraction of ‘if…then’ from the conceptual interactions is not necessary and its a priori determinations (formal ones) are grounded in an individuated dynamic vector field. Or not because in saying that I may have presupposed a manifestation -that of saying that logic emerges empirically. We do not wish to say that, we only wish to show the vectors for logic. In this sense surely the point stands. If we bracket off the a priori if…then (the mathematical) we are at least allowed to note that what we can logical operations can be grounded in the dynamic vector field. What do we mean by this? Again the vector field isn’t just the inside looking out, it is prior to that, it is all feelings, sights, perceptions, sensations even calling them anything. It has elsewhere been called the greater sensorium, but even this is too much. The breakdown into internal/external is itself a comprehension of the vector field. Logic is enabled by the multiplicity of vector field occurrences. The way the vector field behaves means these points (individuated themselves (us/animals etc)) learn the regularities of the field which generates namings and relations (logic). Two points i) abstraction occurs on the back of naming/relations of implanted into the vector field (it is noted that since the same ‘if…then’ relation obtains variously xs and ys can substitute for ‘raining’ and ‘wet’ etc) ii) logic as a reified accretion feeds back on itself and presents a seemingly a priori system.
The vector field behaves in such a way as to enable concepts that facilitate logical abstraction. The vectors for this are the observations of the relations between the concepts as applied to the vector field. Logic feeds off this lower level of implantation into the ‘solid’ vector field to be ‘Logic’ which is itself and accretion or egregore.