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Real World and Ideal World

The Real World, the domain of real beings, is the material world. It is in this World only that processes can take place, and they do indeed take place all the time : The Real World is thoroughly dynamic. It is the world we live in, including all the acts of thinking, which are the result of material processes taking place in material structures, brains.
All the things in this Real World are OBJECTIVE, which means that they exist, and are what they are, irrespective of being thought about or being observed.
Some say that quantum mechanical entities, like electrons, are an exception, but according to me they are objective too (because we can investigate their properties), although they seem to be deficient beings, beings that are not completely determined (Even the assertion of their non-objectivity is, by the way, objectively meant).

But besides the things of the Real World, the material things, we also have 'things' like mathematical structures, for instance the Mandelbrot fractal, which is a geometrical pattern (See the figures, each showing a fragment of this 'Mandelbrot-landscape') and they are clearly immaterial, but nevertheless OBJECTIVE, because they turn out to be what they are, and can be investigated in order to assess their properties.
I have myself investigated the above mentioned Mandelbrot fractal, which shows a remarkable structure. It is a structure generated by an abstract dynamical system according to the logic of mathematical deduction. As soon as the formula (= the prescription) for its generation is set, the ideal (deduction) 'process' starts, and goes its way beyond our control. So it is what it is, and was what it was, independent of mathematicians being there. It turns out to possess an intimate delicate and complex structure in which several regularities can be discovered. In a way we can observe and experiment with it. In fact the Mandelbrot fractal is a four-dimensional object of which we can investigate several slices in order to obtain an insight into its complete structure. It turns out to be infinitely detailed.

This objectivity applies to every mathematical object whatsoever. The same goes for logical relations, which of course are closely connected to mathematical ones.
So we have found a domain of immaterial structures that are nevertheless objective in (their) nature, and this fact necessitates the postulation of a 'Second World' : The Domain of ideal, (and thus) immaterial beings, the Ideal World (or Ideal Sphere of Being), consisting of these static immaterial patterns, which are connected by (or maybe consist of) logical relations.
The Laws of Nature, and also the special dynamical laws (governing particular dynamical systems, like chemical reaction systems) are, in their ABSTRACT (and thus mathematical) form, inhabitants of that Ideal World.
The relation of the Real World with the Ideal World could perhaps be viewed as a simulation process. This asks of course for more investigation, which we however will not carry out in this dissertation.
How do we make contact with this Ideal World, how can we get knowledge of those immaterial structures?
In a preliminary fashion we could say : We can make contact with that World by recreating the relevant structures (the structures of that world), and we perform this by doing mathematics and logic.

Remark : On several occasions in this website I have objected against the existence of an immaterial soul in animals and especially in humans. How does this square with my postulation of a world consisting of immaterial beings?
Well, an immaterial soul is (by its proponents) said to exist in the Real World, because it is supposed to exist in, say, a human being, while the immaterial structures we spoke about above are not existing as such in the Real World, but in a totally different World, the Ideal World.
In the Real World immaterial things are just the result of abstraction (by us), they do not exist as such : The Real World is ontologically homogeneous (not heterogeneous). Also the Ideal World is ontologically homogeneous.

The Universal

In principle it is possible that a same Identity (Essence), i.e. a same Dynamical Law, manifests itself at more than one location, for example

• An Identity ID at space location A,

• An Identity ID at space location B, and

• An Identity ID at space location C.

But if we consider the uniform [NOTE 1] things (Totalities) 'themselves', thus the things in their appearance as things [NOTE 2], or, stated more precisely, when we consider the 'phenotypical expressions' of their identities, and place them in certain classes on the basis of phenotypical similarity [NOTE 3], then we obtain terms which, each for themselves, refer to a collection of uniform things which are similar, terms which are the result of a 'phenomenological' classification. This can also be applied to properties (and to the things having those properties, from the viewpoint of those properties). The following example will clarify this.
The collection of all the individual soldiers living now, but also who has lived in the past and who will live in the future, is a class, a type. We place them in the class SOLDIER (remember the universal soldier of Donovan!) because of certain similar properties. By establishing the Universal (in this case), we don't use the term ARMY, because an army is, with respect to being a soldier, only an accidental collection (of soldiers), established by political and national discriminations and decision-making. But of course the collection of all armies is a class and is signified by the (universal) term ARMY.
A term signifying a class (a collection, but not an accidental collection) implies a 'one-over-many' (one term, signifying many items).
We now can discriminate three cases of signification. Each of these signification cases contains however, as it seems, two subcases :

(a) The term signifies some one content, and as such it could perhaps signify a universal (residing somewhere in the extra- or intramental world).
(b) The term ultimately signifies a collection of discrete and concrete things.

In the examples to follow, for convenience only two or three significata are mentioned in the case where the reference is, not to a universal as such, but to discrete concrete things. These two or three significata are however not the only members of the collection of things to which the reference is made. The reference is of course made to the whole relevant collection, which should not be an accidental collection, but a whole class that is a class in virtue of intrinsic reasons.
Let's now elaborate on the three distinguishable cases of signification by a term that is supposed to be related to a universal :

1. If such a term (on the basis of similarity, it is true) refers to, phenomenologically, after all different uniform beings (limiting ourselves to these), say to crystals of different materials, and moreover having different intrinsic shapes, for example a Sulphur crystal and a common salt crystal, then that which is signified by such a term (the significatum ) cannot be ONE item, i.e. the ONE term does not refer to ONE item (The significatum is not ONE in number). This means that the term does not refer to something (i.e. to some-one-thing). And this is equivalent to the assessment that such a 'universal' to which that one term would refer, does not exist independently of our thinking. In this case only the term is universal. This term could read : CRYSTAL. In a classical context such is for example the term HUMAN. This term, as a sign, refers either to Socrates, or to Plato, or... etc.

2. But (considering a case ) if the uniform things (a multitude thus), referred to by ONE term, would be phenomenologically identical, i.e. looking exactly the same, then it is still the case that ONE term refers to several (i.e. more than one) items, for instance a NaCl (= Sodium Chloride, common salt) crystal and a KCl (= Potassium Chloride) crystal. Both can be colorless, and both can have a cubic form (yet they are essentially different, having different identities, because their chemical composition differs). The term then refers (in this case) either to the NaCl crystal, or to the KCl crystal. Also in this case a real existence of a universal (an existence independent of our thinking) is out of the question, because, again, the term does not refer to some-one-thing (i.e. to something). In this case the universal could be signified by the term CUBICALLY SHAPED CHLORIDE CRYSTAL, but as such it is dependent on, and residing in, the intellect, while as a sign referring to many concrete things.

3. But if ONE term T refers to several uniform things, A, B and C, all having however precisely the same Identity -- let us call it ID -- , thus governed by precisely the same dynamical law, then T still refers to the Real World, and thus the ONE term T still refers to more than one item, namely A, B and C, and thus the term T, signifying a universal-in-the-Real-World is still out of the question (i.e. whatever T signifies, it does not signify such a universal). A, B and C could for example be : three crystals of the same sort (the same crystal species), say, three crystal individuals of NaCl (common salt) not necessarily looking the same. The term COMMON SALT CRYSTAL(S) then refers either to this crystal (pointed to with the finger), or to the other one, or to ... etc. The term COMMON SALT CRYSTAL(S) usually refers to all existing, having existed and in the future existing, common salt crystals, but this also is a collection of beings (things, in this case crystals), and thus a multitude of beings. But if in this last case (case 3) one refers to the Ideal World, and this we can do with the term ID (and implicitly also with the term T [NOTE 4]), then the ONE term does indeed refer to ONE item, namely the (relevant) dynamical law taken formally (as a mathematical structure, residing as such in the Ideal World. In this World all logically consistent mathematical and logical relations and metarelations [NOTE 5] do exist by themselves). In the Ideal World the Identity ID cannot occur as a numerical multitude, because in this domain copying is impossible. The reason for this is that the copying process requires a material context (the copies must be held spatially separated). The above described case of an Identity ID being present at location A, as well as at location B and also at location C, concerning the uniform things A, B and C, was concerned with the Real World. In that World it is possible that copies are being formed of ID.

As such the universal, with respect to real beings, exclusively exists in the mind, and is in that form a (ONE) sign -- a natural sign, that can be expressed, by speech or in writing, by a conventional sign -- signifying many items. The sign (in the context of a one-over-many, i.e. in its function of signification) is always universal, and in the mind, while that which is signified by it either also is in the mind, or outside the mind. The mental sign is a human-bound (or, more general, knower-bound) item, but nonetheless a symbolic representation of a multitude (or potential multitude) of mental or extramental items (including states). The biological -- because a human is an organism -- symbolism (mental signs, natural signs) is being transformed in an arbitrary symbolism (conventional signs) in the relevant language of speech and writing.
The mental sign (and also the conventional sign) is in itself (i.e. not in its significative function) : a neural activation pattern (and when it is a conventional sign : moreover a resulting soundpattern or a graphic pattern). The meaning of a symbol, thus that for which it stands, is extrinsic to the symbol itself. Meaning is generated by a historical and also by a here-and-now context. So the sign, as one-over-many (thus in its function of one-over-many) is a universal, and this (universal) is only in the mind. This "only in the mind", expressing the ontological status of the Universal, is equivalent to the just mentioned fact that the meaning of the sign is extrinsic to the sign. The sign is ONE, but that which is signified (the significatum) is, at least potentially, a multitude.

Having established the ontological status ('seat') of the Universal, we now know that the Universal with respect to real beings neither is seated in the Real (objective) World, nor seated in the Ideal (also objective) World, as universal. The Universal is an epistemological (= concerning our way of knowing things) item, not an ontological (= concerning how things are in themselves, according to nature) item.

The Universal opposes the Singular, the Particular and that which is Individual

In most cases we can do with the term INDIVIDUAL (i.e. the term suffices in most considerations), which encloses in a way the other aspects (of particularity and of singularity).
In a logical context we can talk (if desired) about the ' general individual ', namely in those cases where we do want to express the aspect of individuality, but without implying contingency. So we can talk about " the individual human " meaning either Socrates or Plato or Petrus or....etc., and not only (pointing to) Socrates. In the same way we can talk about "the general animal individual", meaning this snail, or that snail, or that wolf, or that horse, or ... . In still a more general sense we can talk about "the general individual just like that", meaning this molecule, or that crystal, or that horse, or Socrates, or ... .

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