Logic
Theory of formal tools for acquiring knowledge
Part II

Prolegomena to a genuine theory of the formal elements and structures necessary to acquire knowledge
On our way to an Intentional Logic
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The Conditions for an Intentional Logic
Introduction.
In this document we investigate the conditions necessary for an Intentional Logic to be plausible at all. Only then we can systematically lay down such a Logic, and claim that it, as Logic, should replace modern mathematical Logic (with which we do not say that modern mathematical logic is false, but simply that it is not Logic, if we mean by the latter an investigation into the formal tools of human knowledge. Mathematical 'logic' is then a special mathematical discipline, and a very valuable one).
With "conditions necessary for an Intentional Logic" we mean that we must first find out whether the presuppositions (metaphysical, epistemological and biological) of an Intentional Logic are at all reasonable, before we will embark on a systematic development of such a Logic. Of course, it cannot be avoided that we, in order to find out about these presuppositions, must already do (some) intentional logic. For example, we must devote a lot of attention to the way of development of a concept in a knower. In connection with this, we must decide whether the idea of formal sign, which is the alleged result of such a development, is sound. Further, we must decide upon the status of the 'logical' entities that are as such presented by mathematical Logic. Especially the status of propositions (which play such big role in mathematicl logic) as logical entities must be investigated. So we must anticipate important issues already properly belonging to the first two main divisions of Intentional Logic :  concepts and propositions. In all this, we must ask ourselves what in fact knowledge is. And all this will take a long breath, but it must be done.
For the idea of an Intentional Logic we are indebted to Henry VEATCH, Intentional Logic, 1952, where we have consulted the 1970 edition. We are also indebted to John WILD, Introduction to Realistic Philosophy, 1948.
Logic and metaphysics.
In the following we are trying to answer the question :  is Logic, insofar as it treats of the way of thinking about things (first of all) in extramental reality, based on Metaphysics, or is Metaphysics based on Logic? It is plausible to hold that Metaphysics cannot be based on Logic, because then Metaphysics is dependent on the human way of thinking. So Logic is based on metaphysics (as representing the basic ontological structure of extramental reality). But on which metaphysics? There are many proposed metaphysics. This is what we will try to find out (as good as it gets).
In order to do this we attempt to set up a Logic, that is about the basic and formal (in contrast to psychological) ways of human thinking about things existing (first of all) in extramental reality, a Logic as neutral as possible with respect to metaphysical presuppositions, and then see what metaphysics is in fact presupposed by such a Logic. If it turns out to be the substance-accident metaphysics, then we have obtained yet another support for it (the other support consisted in the finding that the general and relevant results of natural science are at least compatible with this substant-accident metaphysics, especially when we involve dynamical systems theory).
If this metaphysics does not fit in well with the established Logic, then either this metaphysics must be abandoned or amended, or the established Logic must be amended (or not recognized as genuine logic) or abandoned, and replaced by another. But whatever Logic we establish or choose, it must be intentional ( NOTE 14 ),  otherwise it has no relation to extramental reality, and thus to metaphysics. This is demanded by a realistic theory of knowledge as it is accepted on this website. When this demand is not met, it would be a discipline all by itself, that is, a self-contained discipline, like mathematics is. Some mathematical systems can be physically interpreted and then result in a piece of physics. Materially interpreted intentional Logic results in metaphysics.
Intentional Logic and its conditions
Logic, for our purposes, must be such that it be adapted to its subject matter (or, equivalently, to its object), not its subject matter to it.
We must investigate whether the new 'mathematical logic' indeed is the logic we should turn to, or not. Accordingly, the mere fact that Logic has more or less recently been rendered truly mathematical, and hence a tool of remarkable vigor and precision, would not necessarily mean that it had thereby been rendered fit to handle any and all scientific or philosophical problems. To substantiate such a conclusion, it would be necessary to show not merely that Logic had become mathematical, but also that the realities which are the subject matter of philosophy and of the sciences are in turn of such a nature as to lend themselves to such logico-mathematic treatment.
Mathematical Logic disregards intentionality (that is, its connection with reality). And even if reality would itself be totally mathematical, the Logic must still be intentional. That is to say, even if reality were mathematical, this reality would still have to be intended through properly logical instruments.
Preconditions for a Logic that is ultimately about  k n o w i n g  things in extramental reality in the sense that it is ultimately about  t e r m s  of first intention refering to reality.
A precondition for such a Logic to be meaningfull is that it operates withing a realistic theory of knowledge. We have discussed this theory in the document  The Realistic View of Knowledge  in the first Series of documents in First Part of website and in Part I of the present Part ( = Fifth) of Website Realistic Theory of Knowledge in Aristotelian Metaphysics .  Here we will be brief bout it.  Its two theses are : This realistic theory of knowledge seems pretentious, but it isn't. It opposes views that assert that our knowledge of 'reality' (whatever that may be) results in a reality-known which (reality) is, also as regards qualitative content, although not on the individual knower as individual, dependent on the general structure of the cognitive apparatus (its logical as well as its physiological tools) of the knower. This means that the World, as we can come to know it, always remains inextricably 'colored' by certain features of the cognitive apparatus.
It could even be assumed by this non-realistic view of knowledge that reality is not even there in the absence of (human) knowers. So both versions of such a view, and certainly also all other versions of it, hold that reality is subjective with respect to man.
Because all features of the World (whether this world as such or as known) are observed to be integrated into one single coherent whole -- the Universe -- by means of causality, interactions, etc., so that there seem to be  no  fundamentally disparate parts of the World, that is, parts that cannot have anything to do with each other, parts that cannot, even in principle, interact, because of all this, a world that is  partly  subjective (that is, irretrievably subjective) and  partly  not, seems very unlikely. See for this also further below.  So it is reasonable to say, that if known-reality is subjective, then it must be totally subjective, and, moreover, we can then also not speak of a division into known-reality which is (totally) subjective, and not-known reality in the sense of not knowable, even in principle, which is objective (how do we know that there are unknowable things and that they are as they are?).
So the World is either subjective or objective, where 'objective' means that although some aspects of the content of our knowledge are subjective, they can be recognized or exposed as being subjective, and its objective causes detected. So we can purify our knowledge from subjective elements, which were not genuine subjective elements, but elements wrongly interpreted.

So again, the world is either subjective or objectrive. Any non-realistic theory of knowledge thus asserts that our propositions about the World are irretrievably subjective (resulting in the World to be subjective). But it cannot assert this, because it implicitly makes an exception :  Its thesis, saying that all propositions about the World are subjective, is itself meant to be an  objective  proposition about some state of affairs in the World, namely about the knowing process and especially the content and status of its results. So while the content of their claim is about subjectivity, the intention is supposed to be objective. If not, their assertion would be merely subjective, while it was meant to express that the world is just so  ( is  just so)  that all knowledge of it is subjective. So any non-realistic theory of knowledge destroys itself, because it contains an internal inconsistency. And this means that the adoption of a realistic theory of knowledge is not a metaphysical presupposition, but a logical necessity.

A second precondition for a Logic as characterized above, is that it must be  intentional.  This follows more or less from the first precondition :  The cognitive tools must be able to 'grab' or apprehend the really existing things. They must be fit to deal with reality (as it is in itself).

Perhaps a third precondition for this Logic is that we should assume that in extramental reality (that is, reality that can be known by intramental tools [and where they are 'intramental' only as to their cognitive function] )  only individuals exist.

From these preconditions (and perhaps already all of it from the first precondition [realistic view of knowledge] )  follow certain things regarding cognition, and eventually a Logic will follow. And then we must see what sort of Logic this is, and, especially, what brand of metaphysics it presupposes (it must presuppose one or another metaphysics, because we have demanded that our Logic must be intentional, i.e. aiming at reality, that is, as a tool of knowing it. This reality is then of course presupposed by such a Logic. And it is not sufficient that reality as such is presupposed, but a reality with a definite structure, because our Logic is supposed to be a tool of knowing what this reality precisely is, that is, what its structure is [and this structure is first of all its ontological structure, as such explained by some metaphysics] ).

One could, of course, redefine  ' knowledge ',  and to restrict its application only to certain types of responses of organisms to their environment. But this is a physical interaction which changes both, implying that knowledge could not be objective. One can simly refuse to talk about a reality to be known as it is in itself, and can insist on talking only about problem-solving. And for certain restricted and specialized types of scientific investigation such a redefinition and confinement might prove quite fruitful. But how about knowledge of things as they are really and in themselves, as it is suggested by the above two statements of the Realistic View of Knowledge? If one denies such a knowledge to be possible or relevant one would certainly have to profess to  know  that this sense of knowledge is not relevant or possible. But this knowing is exactly the kind of knowledge being denied :  objective knowledge. So again, any non-realistic view of knowledge contains a contradiction.
Therefore we must stick to conceding the possibility of coming to know things as they are in themselves. And this knowledge involves a cognitive relation expressing a formal identity between knower and known, for if it be possible for a human knower to know an independently real object, and to know it as it thus really is in itself and apart from such cognitive activity, then the knower must both be able to know  it  (viz., the object) and must be able to  know  it. To say that he must be able to know  it  means merely that he must know that object itself, and not a mere likeness of it or copy of it or idea of it or image of it, but it itself. And to say that he must be able to  know  it means that he is not merely responding to the object or reacting to it or being acted upon by it or undergoing its influence. Instead, he simply knows it.
How objective knowledge might be accomplished
In Part I of the present Part ( = Fifth) of Website in the section Realistic Theory of Knowledge in Aristotelian Metaphysics  we spoke about a possible conception of the asserted formal identity between knower and known. Only such an identity guarantees that the thing is known as it is in itself. But what precisely is then this identity? For this we must turn to the logical instruments (made possible by physiological and psychological processes in the human body). That there are such instruments would seem to be evidenced by the fact that we come to know things in  concepts  and through  propositions  and by means of  arguments  or demonstrations. And that these instruments are instruments of cognitive identification is evidenced by the fact that any concept is necessarily a concept  of  something, any proposition a proposition  about  something, any argument an argument in proof or demonstration  of  something.
Indeed, to say that a concept is  of  something does not mean that the concept merely  resembles  what it is of, or is similar to it, or copies it, or anything of the sort, because we then would have two entities, and thus would not have the identity required for knowing things as they are in themselves. What the concept is of,  is,  or becomes, the very  content  of the concept itself. Likewise, a proposition and what it propounds, a demonstration and what it demonstrates are certainly not related to one another by any relation of similarity or of copy to original. On the contrary, what the proposition propounds is in the proposition itself as part and parcel of it. It is not outside it as something which the proposition somehow copies or resembles, because, again, we then would have two things, not an identity (VEATCH, p.10). But, of course we do not become wooden by knowing wood, nor does the wood become a physiological or psychological process. It is rather a case of the physiological and psychological operations, that go on within the knowing organism, giving rise to certain cognitive media or instruments in and through which the relation of identity with the object comes about. These media are just such things as concepts, propositions, and arguments.
Knowing does not mean that we are coming to know these concepts, propositions, and arguments, but means that we come to know things by means of these logical tools.

Although the identity of the object (is thing or event intended, or an aspect of such a thing or event intended) as it really is with the content of the concept, proposition, or argument, is absolutely required for getting things known as they are in themselves, it nevertheless is hard to grasp :  In knowing the object we do not become materially united with it in the sense that the object is moved into us and becomes part of our being. This indeed means that the identity is only formal. But nevertheless this is a rather cavalier assumption, at least at first sight.
Identity between two spatially and materially separated things -- knower and known -- can only come about by some immaterial formal content. In the known object this content is, because it is just a content, a content of some material thing resulting in, say, a piece of wood. But when it becomes also content of a concept, it does not turn us, or a part of us, into a piece of wood. Why not? The only thing we can come up with, in answering this question, is that that of which the content of a concept  is  the content of a concept, is totally different from that of which the content of a material thing (the thing known)  is  the content of a material thing (that is, the respective carriers or substrates of such a content are different). In the case of the object this results in (to stick with the example) a piece of wood, while in the case of the concept it results in the  concept of wood.

We see, that as soon as we adhere to the possibility of knowing things as they are in themselves, we must assume  ' formal content of something '  in which "formal content" is not the same as that "something" (otherwise part of us would turn into wood as soon as we know or intend some existing piece of wood), and this is denied by, for instance, Ockhanism (Nominalism). Indeed it seems to be denied by our third precondition  ( 'only individuals exist' ).  We can for the time being respond to this problem by saying that  formal content  does not, all by itself, imply existence (of this content).
Existence only applies to individuals.
And if we deny  formal content  to play a role in philosophical investigation, then we deny the possibility of the mentioned identity, and thus we then deny the possibility of knowing  things-as-they-are-in-themselves  for  all  cases (not only for some cases), and such a vision destroys itself as we have seen above .
First intentions, Second intentions.
The objects of first intention are the objects, the concepts, propositions, and arguments are about.
The objects of second intention are those concepts, propositions, and arguments. That is to say, the objects of second intention are first intentions (or second intentions).
Second intentions say something about first intentions (or second intentions), and it could be that second intentions make first intentions to be signs of things that are not signs.
The nature of first intentions.
Accepting the realistic view of knowledge has penetrating consquences, as we saw above in the case of then having to accept  formal contents  as such (that is, acknowledging a real distinction between supposit and essence, for example the real distinction between Socrates and his human nature).
Cognition is a type of awareness. Awareness of something is not the same as being acted upon by that something. For example, the awareness of heat is different from being heated. Hearing is not the same as being subject to air vibrations :  Anything can be subject to air vibrations without, however, hearing a sound. And although what can sound and what can hear are two very different things (one is the efficient cause of the hearing of [by] the other), the actual sounding of the sound and the actual hearing of the sound are one actuality. The formal content of the efficient cause (which latter is a thing insofar as it produces air vibrations) is itself present in the hearer, which (type of) presence we could call  noetic presence  (WILD, J., Introduction to Realistic Philosophy, p.409). And what is noetically present is called  sensible species.
We can now see that noetic presence is quite distinct from physical presence or subjective inherence. What is physically inherent in me as the result of external physical causes alone (such as temporary physiological changes in sense organs), belongs to me and can never give me knowledge of anything outside of me. Hence to confuse a sensible species, like the color yellow, with a physical impression (a physical 'disturbance' of a sense organ), produced by external vibrations or similar causes, leads us into a subjectivism or solipsism which makes any understanding of the facts of knowledge (things known) quite impossible. If to know an object were merely to be physically influenced by that object, every physical thing would know. We must therefore at the very outset recognize an immaterial mode of presence in which it is a case, not so much of an external cause making something physically present in me by a material impression, as a case of an internal act of the knowing faculty making an external object ( = a thing insofar going to be known) noetically present before me by an immaterial species (WILD, Ibid., p.409-410).
This is quite a bold presentation of the alleged state of affairs constituting awareness and knowledge, involving entities like  "internal act of the knowing faculty",  "noetic presence",  "immaterial mode of presence",  etc.  Bold statements, I remind the reader, can also be a sign of unwillingness to go to the bottom of the problem -- for example investigating the most simple sense organs we know of, probably to be found in polyps, medusae, ciliates or even bacteria, could be revealing in this respect. An unwillingness to do this, or (an unwillingness) to take already established relevant (biological) results into (philosophical) account, together with cherished prejudices, is often expressed by the invention of new or differently used terms, such as 'noetic' in 'noetic presence'.
We must, however, admit that a solid understanding of awareness and cognition is still far away, forcing us to stick, for the time being, to the just given exposition. It is, as far as I know, the best we have (especially insofar as it expresses the possibility of objective knowledge), but we should not present it as a final and all-explaining solution of the problem. On the contrary, we should be willing to abandon it, when new evidence against it becomes available. Let us continue (following the theoretical lines of WILD, pp.410, and considering consequences and examples).
If -- now presenting an example of mine -- a crystal is immersed (for a while) in a solvent, it acquires so-called etch figures or marks :  small regular etch pits, impressions so to say, on its facets. Here we can say that the crystal is the substrate for replaceable determinations, and the presence of etch figures is one of them. When having acquired etch figures, the crystal has, as it seems, something of the environment (which is the solvent), but in fact it has nothing of the environment except the results (etch figures) of its interaction with the environment. So the crystal only subjectively has something of the environment, by being the substrate (subject) of the etch figures caused by the solvent. So physically interacting with the environment is subjective. This is evident, when we submerge another species of crystal in the same solvent, namely a(n individual of a) crystal species that is insoluble in this particular solvent. The crystal at most gets wet. And if we submerge an individual of yet another species of crystal, soluble in this same solvent, but a crystal belonging to a different crystal system as our first (soluble) crystal did, then also etch figures appear, but these etch figures are different (from the ones earlier obtained), they are different with respect to their symmetry. The symmetry of etch figures turns out always to be the same as that of the crystals on which they are formed. So the reaction of a crystal with a solvent is indeed  subjective  (in the same way that a Picasso painting has different impacts on different viewers).
So if awareness and cognition want to be objective they cannot be physical.
It is through their possession of the extraordinary cognitive faculties that the animals by sensory awareness, and more especially man, through sensory and rational awareness, are able to overcome the subjective isolation that necessarily attaches to all material entities. Such (material) beings can unite themselves only with those forms and modes of being which are physically inherent in them at a given time. And the nature of these forms and modes making them unifiable with the given material beings is thus restricted and determined by the physical properties of the matter of these material beings, while these beings are isolated from all those entities with which they cannot come into physical contact. This physical contact is established by physical signals such as light. If we, only insofar as we are material beings, look to a star that is a thousand lightyears away from us, we see this star as it was a thousand years ago thanks to the contact with it as it is established by the light, radio, or gravitational signals that were sent by the star [in all directions] and (now, finally) received by us. And when such influences, as we could call them, are actually received by us (as physical bodies), they are at once subjectivized and individuated by the material recipient, so that there is no possibility of genuine union with the other entity -- star -- as it is in itself.  So while we, like any other physical body, can undergo the influence of the star, we, when we consider ourselves to be no more than physical beings, cannot know it as it is in itself.
Each material entity (so also we insofar as we are material) is united only with itself (because what is received is transformed into a part of the recipient, as was the case with crystal in the solvent, where we saw that no part of the environment (solvent) had become a part of the crystal), dwelling within its own restricted limits, completely cut off from the rest, even when it interacts with it.
But through awareness and cognition (meaning that we are no longer speaking of material entities, and thus also not of humans insofar as they are just material entities) this cosmic loneliness is actually overcome. The facts show that we (and probably many higher animals) cannot only be physically affected by things even when they are spatially separated from us (though connected to us by physical signals), but also be  aware  of them, which means being  united  with them (in contrast to just being connected with them). The mentioned crystal was connected to the solvent in virtue of interacting with it (where both are changed as a result), it was not united with it (in the sense of identified with it). When light rays of a faraway star strike our retina, we are connected with this star in virtue of the impact of its radiation, but we are as such not (yet) united with this star. We do not (yet) see it. So sensory awareness ( = sensory cognition) consists in a unification of sense faculty and the object that is (either via its signals, when separated from us, or in the form of direct contact) present at the time of awareness, while in rational cognition, as we have it in man, man can be united in this way with all things, existing at all times (on the basis of presently available clues). Through his understanding of causal sequences he can make the past and future noetically present, though not physically present.

Let us proceed further with expounding sensory cognition.
If we try, in order to explain sensory cognition, to get along with (just) physical causes plus the physical effects in the sense organ (which definitely take place in sensory cognition), we have an impression subjectively inhering in the organ which is (as should be conceded by this type of explanation) at best only like the external quality (of an object outside the mind), and therefore not knowledge but only physical assimilation (like the etch figures in a crystal). This kind of explanation can be called representationalism (WILD, p.414). This (explanation) is open to two objections.

First, as already indicated, we can never know the object at all, but only something supposedly similar to it, representing it in the mind. And similarity, while being not identity, does not then necessarily be partial identity. Earlier we have found out that similarity between a this and a that is not necessarily implying a duality, in the sense that similar things would have (1) something in common (something that is repeated), and (2) something that one of them has, while the other has not. Similarity could just as well exist between things that have no  parts  in common, as our earlier diagram (previous document) had illustrated :
So similarity between the image and the object does not guarantee that the image really possesses something of the object. It does not guarantee that we can actually cognitively grab or apprehend the object. So again, if the thing to be known is just represented in the mind by some image, we can never (in all cases) know the object as it is in itself, but only something supposedly similar to it (See WILD, p.414).
Of course it is not at all clear what precisely is meant (by WILD) with :  "we ... [then] know ... something supposedly similar to it [that is, to the extramental object to be known]".  Can we know, and not merely have, mental images (of things)?  Also here we have to  be  such images in order to know them. So we see that by replacing the object by a mental image in order to explain sensory cognition, we merely shift the problem of knowledge instead of solving it  ( This is indeed what WILD is telling us).
Of course representationalism could hold that although the image is caused by an external object, the image is all we have. In this way the World-as-it-is-known  is  qua content made dependent on the knower. What we can know is then :  just what images result during the interaction of the sense organ (interaction in the case of touch), or (what images result) during the action of the object (for example via the emission of light) upon the sense organ. All this results in subjective knowledge (subjective with respect to man that is, not with respect to the individual).
If representationalism is not prepared to grant this, then it will hold that we know extramental things through images (of them). But how can we ever jump out of our minds to compare those images with what is outside, and thus establish any similarity? This is impossible, because all we have are the representations (mental images) of things sensed, not the things themselves.

Secondly (that is, a second objection to representationalism), the physical presence of the image is either also its noetic presence, or it is not (i.e. the presence of a physical image does not necessarily entail a noetic presence).
Noetic presence establishes the union, instead of merely a connection, where the latter means the immediate subjectification and individuation and thus a subjective possession of the effect following upon the influence (as we saw in the case of the etch figures of a crystal), instead of being that (external) thing itself.
If we say the former (physical presence of image is always also its noetic presence) we cannot explain two sets of evident facts. The first is that a non-living being, like a bar of metal, in which heat is physically present, certainly does not sense the heat. So here the physical presence does not automatically imply a noetic presence. The second is, that many qualities, like radiowaves, may physically inhere in us without our sensing them. Also here, physical presence does not necessarily imply noetic presence. So we are forced to admit that the mere physical presence of the impression (image) in us does not constitute (all by itself) knowledge. But then we have simply postponed the whole problem and have not explained it at all (WILD, p.414).

In the present context (sensory cognition) it is important to be clear about quality and qualitative content, as that which can be sensed or detected by a sensory organism.
The  color  (to take an example) of something is a quality. It is not necessarily a replaceable determination of something, but can be. For example :  the color of a plant (considered as a genuine single being, that is, not an aggregate of beings) can change from green to yellow. So the color is in this case a replaceable determination. On the other hand, the color of something can be a necessary essential content of that something, such as the blue color of a copper sulfate crystal (which color cannot change without changing the chemical composition of the crystal) ( NOTE 15 ).
But -- when considering how we perceive an object qua colored -- is it true that a given color (as an example of quality) is objectively and physically present in some external object (as precondition for the color to be sensed), as WILD (p.415) assumes? What exactly is present in a blue copper sulfate crystal? The crystal consists of a three-dimensional periodic array of atoms and atomic groups, connected to each other by chemical bonds. The structure is such that it results in a definite point and space group symmetry of the array. As such there is no color present in the crystal. Only when (sun)light is passed through it or reflected by it, we see the blue color. This blue color (i.e. the absortion of all wavelengths of visible light except a 'window' of more or less short wavelengths) is the result of interactions and energy transfers, scattering and absorption of light inside the crystal. So where is the blue ? (It cannot come out of the 'blue'!).
So far we have considered the crystal as just a system of quantitative relations it seems. However, in Part I (of the present [fifth Part of] website we found out that it is impossible to have, in real things, quantities without qualities. If a crystal (or whatever being for that matter) was totally mathematical it would not be observable. Further, a size or length can only be definite by an alternation of different qualities :  Here, in the object, we have quality X, and here also, but there it is not present anymore, it is replaced by another quality. So there must be quality in the crystal (that is something different than pure mathematical relations). Shape and symmetry (as mathematical 'qualities' )  cannot be observed, that is, as such they are not visible. They are abstract features (and can therefore be treated in geometry, respectively, group theory). And because a copper sulfate crystal  is  observable (visible), it must have qualities. And just like shape and symmetry are not physical parts of the crystal, these qualities are also not physical parts of the crystal, and being  blue  is one of them.

And, to continue our discussion about sensory cognition, this quality blue, physically present in the crystal, is then transmitted via the electromagnetic field from the copper sulfate crystal to the eye, as light energy impresses (interacts with) the retina.
That in order to sense anything the sense organ must be acted upon physically is certain. But then we have the case of receiving a form (such as the form blueness) subjectively :  the form is received in the organic substrate of the organ or organism which senses. From this no objective knowledge comes forth, as explained above. WILD tries to solve this problem by stipulating that the form must be objectively received. And this, according to him, implies that the form must become disattached from the matter of the organ or organism, that is to say, the form, after being brought into the sense organ as a result of the latter being physically affected by the object, and now, as a result, inhering in the organic substrate, must be disattrached from this substrate. And upon disattachment, it should not go to re-inhere in any other alternative substrate in the organism, because then it will be subjective again. So the form must remain  immaterially  present in the sensory faculty.
However, this explanation, although really adressing the problem of objectivity, cannot as such be accepted. The organism is in its entirety a material entity. Said differently, we believe that physical matter, and physical matter alone, can perform the function of life, and with it, the function of sensation (and also of rational cognition), all by itself, provided it has become sufficiently and adequately complex. It is ontologically very implausible that immaterial forms somehow exist in a material context  ( Such an assumption gets, of course, easily off the ground when it is held that man is ontologically dualistic, namely consisting of body and soul). But, if it is not by the presence of immaterial forms, how then is objectivity, and therefore sensory awareness, accomplished by the organism? The answer is, according to me to be sought in the phenomenon of encoding and decoding information. Let's consider an instructive analogy.
When a grammophone record is being produced one starts with a disc covered by a layer of some sort of sealing wax. Having such a disk, one can engrave it by means of a needle. Further, one has a device that transforms music into mechanical vibrations. These vibrations are conducted to the engraving needle, causing the needle to vibrate. As the sealing wax disc rotates the needle engraves the vibrations into the sealing wax. In this way a spiral track is created in the sealing wax. The vibrations of the needle are recorded as a zig-zagging groove in the sealing wax. In this way a grammophone recording is made ( NOTE 16 ).  The so produced record can now be played on an appropriate device (the grammophone) to display the music (using again a needle that will now be caused to vibrate when drawn through the record's zig-zagging groove, and the vibrations of the needle will be transformed back into music).
This whole process is thus one of first encoding music into the wax disc (via the intermediate encoding of it as mechanical vibrations), and then decoding it again by the displaying device.
How must we interpret this ontologically? First of all we must say that the groove in the wax of the record is just a replaceable determination of the wax ( NOTE 17 ).  As such it is no different from the etch figures in a crystal as discussed above. The mechanical vibrations of the engraving needle bring about a spiral zig-zagging groove in the wax. As such this groove is no more than the subjective response of the wax when subjected to the vibrating engraving needle. The wax does not hear or read the music. Grooves cannot exist by themselves, but the grooved wax can. And this grooved wax is just a product that has resulted from the action of the engraving needle upon the wax. The wax has responded to the needle in its own specific way, just like the crystal has responded in its own specific way to the action of the solvent. In both cases (groove, etch pits) the product is just the entity in its state of having undergone the action that came from outside it (the same applies the other way around, that is, to the engraving needle [its wearing], and the solvent [its becoming more concentrated] ).  So insofar as the effect of the action (engraving, etching) of the environment on some entity manifests itself as just a replaceable determination of that entity, the (acting) environment, or relevant aspects of it, is still not felt. How, then, is this latter accomplished? Well, in addition to the groove as just a groove, being an accidental form of the wax, there is another form. This form is the information encoded onto the groove (we say, the groove is modulated). It is the specific pattern of the groove's zig-zags. As long as this information is not read and processed by some device, the zig-zag pattern is also no more than a part or aspect of the accidental form of the wax. But as soon as it can be read by such a device it is genuine information. As such it can be called the 'software', carried by the 'hardware' which is the wax layer. And it is the decoding activity which, according to me, is equivalent to the becoming 'aware' of the music, the hearing of the music. In living beings the decoding machinery is extraordinary complex and sophisticated, involving many complexity levels. Nevertheless our analogy with the grammophone is, I believe, sound. When a crystal is put into a solvent, it reacts in its own way. It produces etch pits that display the crystal's symmetry. As such, information about the crystal is directly given, not encoded. But the etch pits are caused by the acting environment, the solvent, so some information about this solvent must in some way be present in the effect. But we do not see this information. Why? Because it is being encoded in these etch pits. And as long as this information is not retrieved -- decoded -- the crystal does not feel the solvent. In the case of the grammophone record PLUS displaying device things are different. Here the information encoded in the groove is being retrieved -- decoded -- by the displaying device. And only during such decoding we can speak of actually sensing the music, that is, coming to know it, and not (coming to have) some likeness of it. And because it is only the stored information that is being retrieved, not some informed thing, the sensing of the music is objective.
In this way we should, I think, interpret the objective sensory apprehension of formal contents (qualities, essences) as they are in extramental things.

Then we have the problem of the dependence of the quality sensed on the specifics of the sense organ involved. While humans see, say, homogeneously yellow petals of a flower, bees often seem to see a colored pattern on them that guides the insects to the flower's nectar. But this is not a matter of subjectivity, but a matter of different sensitivities. The bee probably can see a part of the ultraviolet wavelengths (while our eyes are not sensitive to them as far as perception [ = decoding information] -- instead of damage -- is concerned). Certainly there will be different colors in such a part of ultraviolet, that is, different parts of the petal will reflect different ultraviolet wavelengths.
But could it be that the same group of wavelengths can produce different perceived colors in different visual organs? We could, for example, imagine that some object is green for a given individual human perceiver, and is calling it "green" when asked, while that same object is red for another person, while he calls it "green". This could occur, but cannot be demonstrated. Therefore we can legitimately call the red as seen by the second person "green", or the green as seen by the first person "red".  They both see the same quality, that's for sure. This same quality can be processed differently by different visual organs (in the broad sense, that is, including the relevant parts of the brain), either in virtue of their different structure, or of some defect or malfunction.
All these cases are not cases of subjectivity, because they can be detected as such :  They are cases of 'objective subjectivity', precisely as in the case of the 'broken' stick partly submerged in the water.
Sense observation ultimately never fails, because when it does (now or then), it will sooner or later be detected by another sense observation.

So what we have so far is that extramental objects can, and do, have qualities, and these qualities can be -- each for themselves -- objectively detected by the sensory apparatus of at least higher animals, that is, the latter can be objectively aware of (sense) qualities insofar as their sense organs are sensitive for that which transmits these qualities. Further we know that awareness of a quality (of an inspected physical body) cannot just be the physical effect of the influence of the inspected physical body on the perceiver, otherwise a steel bar that is heated in a fire would not only get hotter, but would feel the heat, and this is absurd. The effect of the influence is just a genuine part of the receiver and is therefore subjective. In order for a perceived quality to be objective, the receiver must decode it, and after this is accomplished the receiver has become, in a way, the quality. As for sensing the blue copper sulfate crystal :  The blue, which is actually present in the crystal, is encoded (we can also say enfolded) in the light illuminating the crystal. This light interacts with the retina of our eyes, but not in such a way that the retina or other bodily parts of us become blue. The neurological machinery of the faculty of vision now decodes -- retrieves or unfolds -- the blue, i.e. it reads the blue from the coded message. And in doing so we  see  the blue of the crystal. Indeed, generally, nothing happens with the form 'blue' when it is encoded, transmitted, and decoded, that is, the form is not (necessarily) perturbed or distorted during these processes, and therefore it is perceived objectively. The form is now  shared  by the sensing organism and the sensed thing, and this is the relation of  formal identity  in (sensory) cognition (it must be only formal, because the sensing organism cannot become numerically identical to the sensed thing).
Qualities (in the broad sense of formal contents) and, concomitantly, quantities or, generally, mathematical relations, are apprehended by te senses. The proper object of any given sense organ (color for the eye, sound for the ear, etc.) is infallibly and objectively known by means of these sense organs. The concomitant objects of the sense organs (all quantitative and mathematical features) are not always infallibly perceived (as we see it in the case where distant objects appear smaller), but can be corrected by the cooperation of all the senses together, finally resulting in these features also being apprehended objectively as they are in the (external) thing.
The origin and development of the concept.

It is now time to use all these findings for the characterization of the simple (non-complex) natural sign, the concept.
It will be a long discussion, in which, because of their importance, we must sometimes repeat earlier findings. The foregoing discussion about sensory cognition of formal contents as they exist in extramental reality, as well as the ensuing discussion about the formation of the concept on the basis of these apprehended formal contents, are crucial for the evaluation of an Intentional Logic as was first proposed by VEATCH. If we cannot solve the problems presented there, or if our findings turn out to be wrong, we cannot accept such an Intentional Logic. But because we intuitively feel that such a Logic has much to offer, we do not avoid lengthy discussions and repetitions.
A concept of any extramental state of affairs is developing in te mind on the basis of repeated observations of individual extramental things. It is precisely the formal contents of these things that are internalized in the mind according to the above described process of decoding information. What follows is an attempt to describe the process that organizes all these internalized formal contents into one or more concepts.
Let us begin by stating that every sense organ has its proper object (that is that to which it is naturally geared), color for vision, sound for hearing, etc. The apprehension of a quality, however, stops when the ultimate efficient cause of sensation, namely the external thing, vanishes. Further, when I observe a green apple I am aware of its qualities, and concomitantly of its quantities. But what we sense by means of having acquired the qualitative (and, concomitantly, quantitative) forms of the apple, is always this green color of this (say) large apple at this distance from us, and so on. Sensation is always sensation of the individual. But how do we come from here to universal statments and predications, resulting in genuine science? How do we acquire genuine universal concepts, provided we do acquire them? How do we apprehend a genuine (that is, not arbitrary) class of individuals, of which a universal formal content can be predicated? Or, asked differently, how are we able to carry out induction? Does reason has a peculiar object of its own, materially identical to that of the senses (of which the combined proper objects [color, sound, etc.] together with the secondary objects [quantitative features] point to the same material individual thing), but formally distinct (from that of the senses), as WILD, p.452, believes?
In First Part of Website, and also in Part I of the present [ = Fifth Part of] Website, we have argued that scientific induction ( = generalizing findings about individuals) is based on a fundamental presupposition of natural science, namely the Species-Individuum Structure of material things. In it it is supposed that every thing acts according to its intrinsic nature or essence (the acting can be on other things, and so also on our senses). So when we have examined a number of seemingly similar individuals (individual extramental things), we generalize some of their features, resulting in universal concepts like 'wood', 'iron', 'rat', etc. on the basis of these features observed in all investigated individuals. In every single individual observation of a given individual thing we apprehend qualities and quantities (as described above). And having in this way investigated many such individual things, we formulate a universal concept. So we formulate it after detailed and prolonged empirical investigation (experiments, observations in Nature). We do not possess a special mental faculty that directly apprehends a universal feature resulting in the formation of a universal concept. Such a universal concept, as it has gradually been developed empirically and stored in the brain, is as such now a sign for extramental individuals, that is, once formed (either still more or less rudimentary, or already much more developed), it, in turn, can and does point to individuals, namely those which participate in the content (comprehension) of the concept. On the basis of this we select individuals in order to place them in a certain class :  Any individual of which we can legitimately predicate the content of the concept ('this thing here is an apple') will be placed (by us) in the corresponding class. So the universal concept, resulting from conscious or unconscious empirical investigation, is then as such a natural sign pointing to a definite extramental formal content, and with it to existing external concrete individual things possessing this content.
Of course such a sign is not wholly natural, because it is the result of human investigation, but once established, it 'naturally' signifies a certain extramental formal content and designates certain individual existing things. It is itself signified conventionally by a spoken or written word (conventional sign).
But, the natural sign as such is not sufficient to characterize a concept unambiguously (that is, to characterize what a concept [as concept] is). It must be further qualified in order to actually be such a concept, because there are natural signs of things which (signs) are not concepts of these things but are things that point to other things that are either similar to these first things, or are causes of them, or are effects of them. Such signs, which are (also) natural signs, are instrumental signs. They have an objective nature of their own, and do not signify these other things directly (because they are different things, different from those they point to), and thus do not stand in a relation of formal identity with these other things as concepts do.
Those natural signs, on the other hand, which do stand in such a relation, and are thus not instrumental signs, we can call formal signs. They have no nature of their own, their nature simply consists in to be  of,  or to be  about,  something else (they are materially different from 'that somthing else' but formally identical to it).
And not only concepts are formal signs, but also (subject-predicate) propositions and (syllogistic) arguments (demonstrations, proofs). All of them are formal signs, or, equivalently, logical intentions.

We have seen, that the observation of a singular individual thing results in relations of formal identity of sensed qualities (necessarily interweaved with quantitative aspects). For every such quality actually sensed, there is such a relationship. This  having of all the sensible features  is  k n o w  i n g  the (external) thing, but only as an individual here-and-now-thing. We do not yet know whether this thing is truly a self-contained thing or just a fragment of such a thing, or belonging to several different such things :  one or more of its parts (belonging) to one self-contained thing, other parts to other such things. The picture of the status of our observed 'thing' gradually arises after many other things have been observed and compared. So it is in the case of single crystals and organisms, where we more or less easily recognize them as self-contained things, then classify them, resulting in, respectively, a system of minerals (based on chemical composition and intrinsic total symmetry, or on the way of their genesis), and a taxonomic system of organisms (based either on morphological or physiological similarities, or on common ancestry).
In other cases, however, it turns out to be very difficult to decide whether something is a self-contained thing or not, such as twinned crystals, mixed crystals, lichens, tight colonies of biological cells or of (whole) animals, or such things as planets, comets, computers, etc. But little by little we learn to recognize self-contained things and to clearly distinguish them, not only from (just) aggregates (of self-contained things), or from being just fragments (of self-contained things), but also from other self-contained things. We try to find the 'essence' of every such self-contained thing. But this can only be done by comparing them with other things.
In First Part of Website we have found a general characterization of the Essence of a self-contained thing :  It is the dynamical law of that dynamical system that had generated, or could have generated, that thing. Much philosophical research was necessary to establish this, and still many problems remain. And although such a dynamical law cannot in most cases be (already) actually formulated (that is, is not yet known), it often is represented in the thing by a set of observable features that have resulted directly from this law. Such a set of features thus can at least represent the Essence of the self-contained thing. An example is the  Space Group (symmetry) PLUS Chemical Composition  which characterizes a given crystal species (which symmetry plus composition is a direct effect of the action of some specific dynamical law, here, one or another crystallization law). But also such observable features (chemical composition observed in chemical analysis, total symmetry observed in X-ray diffraction techniques), able to represent the Essence (which is some dynamical law, such as a crystallization law) of the given thing are, in many other cases, hard to find.
All this means that our idea of the Essence of given things -- albeit just in terms of observable representatives, that is, even if we are already satisfied in having found, although not the Essence itself (or, we could say, the genotypical Essence), its observable representative (the phenotypic Essence) -- is only gradually formed in the knowing mind. It is certainly not directly apprehended by some special cognitive faculty of ours, as some philosophers assert (for example WILD, pp.450). In establishing essences, the presupposition of the Species-Individuum Structure of material beings is always, albeit implicitly, present, and in holding that presupposition we carry out induction :  the generalizing of individual findings. This generalizing, resulting in the reinforcement or consolidation of the relevant concept's content until now formed, and the determination of that concept's extension, is always subject to error, and can never be proved. It can only be more and more strenghened by additional observations.
Not only things are implicitly classified in this way by every knower and explicitly by the scientist, but also qualities. However, it usually takes a long time and much effort to characterize particular qualities as to what they are. A good example is energy, which is a certain state in which a thing finds itself to be in ('this particle has [so and so much] energy'). It has turned out hard to exactly define energy. It is said that energy is the capability of doing work (see our documents on Thermodynamics in Fourth Part of Website ),  but not all energies can deliver work, as was found out in the case of heat energy :  Only a part of it can deliver work, the rest is dissipated. What is needed (in order to deliver work) is an energy difference (energy fall), for example a hot and cold physical body. But also with respect to other qualities it is often hard to establish their intrinsic nature, for example 'red'.  To characterize the latter in terms of wavelength of electromagnetic radiation is not enough, because radiation itself is not colored. But also, in order to form the concept  ' red ',  the quality must be observed and investigated in many different things and in many different circumstances. Therefore we cannot say, as does WILD, p.452, that :

Reason apprehends the very same thing (materially) which sense apprehends, but it grasps something in this thing (formally) which sense cannot grasp, either the essence alone by itself or the accident alone by itself. The object of reason is not another  t h i n g  existing separately from the sensible thing. It grasps this very thing or some accident of it  a b s t r a c t l y  a s  i t  i s  i n  i t s e l f,  with nothing else added or subtracted. Sense cannot do this, because it always grasps a concrete manifold, materially confused together.
We agree that  "sense ... always grasps a concrete manifold, materially confused together",  but have explained how one proceeds from this to universal knowledge, not by means of a special faculty that has a universal essence (of a thing or of a quality) as its peculiar object (such as the apple itself, or the greenness as such, "with everything irrelevant or extraneous omitted"), but by means of repeated observation, and then generalizing as best as one can (unconsciously or consciously).

We have explained induction and indicated what is presupposed by it (just presupposed, not demonstrated) :  the Species-Individuum Structure of material beings. As such it is the presupposition that every material being is catallel, that is, in every material real being (self-contained or not) there is a formal content that permanently (as long as the thing exists at all) determines an indeterminate material substrate. In the case of a quality (or any other accident) we also have to do with a formal content determining a material substrate, but in this case it does not necessarily permanently determine it (it can be replaced by another such content while the thing itself remains existent), and the substrate is not (as it was in the first case) totally undetermined. Also aggregates (of self-contained concrete things) have a Species-Individuum Structure (SIS), but then only in an analogous way.
Does all this mean that universals (represented by the 'species' part of the SIS) do exist in extramental reality? Not necessarily. It is reasonable to assert that in extramental reality only individual things (aggregates and substances) occur. The formal contents (essence, properties and accidents) cannot exist, save as residing in individual things, and that makes them individual (they only become universals when we imagine ourselves that we have somehow managed to actually separate the formal contents from their substrates, which imagination is possible, but not the actual carrying out of the separation itself). So in extramental reality all formal contents are, though not individuals, individual. What is universal is only the  term  denoting many individuals related to each other in some way. So we do not need a special faculty that can apprehend universal essences in extramental things, because such essences are not there in extramental reality. With respect to formal contents, there are only individual formal contents in extramental reality. And these individual formal contents can be grasped by sense observation, as I have explained above. And now repeated observation and comparison (consciously or unconsciously) will render us capable of singling out groups of formal contents (which groups we can call essences) enabling us to form classes. Such a class is a set of individual (fully-fledged) things and constitutes the denotation of the concept, that is, constitute the meaning of that concept in terms of its extension. The set of individuals itself is not the meaning of the concept but its range (its range or domain of application in extramental reality). The criterion to allow a given (that is, selected) individual to be a member of such a named set (for example 'animal') is some individual formal content in it (which can be observed). If an individual possesses this particular formal content, then we make it a member of the named set (class). If it doesn't possess it, we do not allow it to be a member of that named set.
So again, formal contents do exist in extramental reality, but (there) they are always individual. This view can be called moderate nominalism, or (equivalently) conceptualism (universals do not exist in extramental reality, but they do exist in the mind in the form of certain signs).
The realistic theory of WILD says that reason has its own object, a universal essence or a quality as such. We have already shown that a universal essence, and also a universal quality, do not exist as such, that is, as universal, in extramental reality. The content of a given essence or of a given quality is, as it exists in extramental reality, individual, and can thus be apprehended by the senses..
But this means that reason has no peculiar object in extramental reality, that is, it has no object whatsoever. While calling it (still) the object of reason, WILD now identifies it with the abstracting activity of reason :  Some formal content, individually existing in some given extramental individual being is (by the activity of reason) abstracted from its material substrate, resulting in this formal content to become a universal. We have, however, already seen that this is not how things go. The universal is not formed by abstracting it from its substrate (and then predicated of many other individuals), but is formed by often a long process of repeated observations and comparisons as explained above. Also in this sense reason has no special peculiar object (like any sense organ has).
When a concept (which as such is a universal) is finally formed it becomes  a  sign  (a natural sign, itself indicated by a word or words). And because such a sign is not something that came spontaneously and necessarily into existence, but only after much had been done (think of the concept of energy for example), it can as such not, it seems, be a sign in the sense of a truly intentional sign, because as such it doesn't seem to be a natural entity but a forged one. But because it in fact entirely consists of, or is reducible to, (the results of) actual sense observations, it must have the same character as the results of individual sense observations, and this character is its formal identity with something in the things taken disjunctively. So the concept is a (natural) intentional sign after all! As such it always refers directly to certain formal contents in things, and this means that we have to do with genuine signification, that is a meaning (of the sign) not beforehand restricted by some context. When we add such a context, for example when we let the concept figure in a definite proposition which is such that it narrows down the meaning of it, resulting in the concept's actual meaning in this present context, we say that the intrinsic meaning of the concept becomes restricted (there exist contexts which do not restrict the meaning of the term or concept). When the sign figures as a subject in a proposition about things, the subject term, whether the applied context (the proposition) does restrict the meaning of the (subject) term or not, refers to a thing (as in  ' man is an animal ',  which expression in fact means that every man can be characterized by possessing the feature 'animality'), which implies that the term  ' man '  (as in the above proposition) does not in fact  s i g n i f y  any concrete individual man (because  ' man '  s i g n i f i e s  only the essence of these individuals), but can  s t a n d  f o r  these individuals, that is, we have to do here with supposition (suppositio) or, equivalently, designation. And, as has been said, the total set of these individuals is the range, domain, or extension of the concept  ' man '.  In the present case the proposition  ' man is an animal '  does not restrict the meaning of  ' man ',  that is, does not exclude any individual from the domain or extension of the concept. Here we have a case of, what is called, natural supposition. If the context does exclude certain individuals from the extension of the concept, such as in  ' all white man live in the western hemisphere '  (whether this assertion is true or not), we have a case of so-called accidental supposition with respect to the concept  ' man ',  because here this term does not refer to its full extension but to only a part of it, as a result of the added adjective  ' white ',  which excludes all colored men.

So in summarizing, I agree with the main ontological tenets of WILD, that is to say, the status of the universal, or, equivalently, the concept. I disagree, however, as regards the way a concept is formed, and also how sensory awareness comes about. The universal is not the result of a special ability of the intellect (abstraction of a 'pre-universal' from the extramental matter-form composite [prime matter -- substantial form, or substance accident] and then 'see' whether it can be predicated of many individuals, resulting in a universal when it can be so predicated), but the result of many awarenesses of extramental formal contents on many occasions. Both for me and for WILD the universal is not a separate thing that exists by itself, but is a relation (which is perfectly expressed by calling it a [formal] sign). The foundation of this relation is the formal content (s.l.) as it is found expressed in the Categories. And when it is predicable of, in principle, an indefinite number of (possible) extramental material individuals, it is a universal concept. And it can be predicable in a number of different ways (kinds of universal relations) of such an individual, namely as genus, difference, species ( = genus and difference together), necessary accident (proprium), or contingent accident (accidens). These five universal relations, or predicables, exist only in the mind. What is related by these relations is the formal content (s.l.) (belonging to one or another Category) as it is formed (in the way explained above) in the mind  AND  the given individual material thing as it exists outside the mind ( NOTE 18 ).
In this way the universal concept can stand for such individuals and signify some formal content in them.
The naturalness of a universal concept as sign stems from the many single observations and experiences that have preceded it and constituted it. In language it is, then, finaly expressed by a word (conventional sign). The natural sign, as conceived here, can also be called formal sign (distinguishing it from an instrumental sign, also a natural sign), or (can be called) an intention.
The difference between the opinion of mine and that of WILD as regards the formation of a universal concept is important, because in my view an ontological dualism in man (body and soul) is avoided (it was also avoided when considering sensory cognition). The formal identity of content in sensory cognition is, according to me, describable as a retrieval or decoding of (qualitative) information about the external thing, information that was encoded or enfolded by and in the medium (electromagnetic field in the case of vision, air in the case of hearing). The formation, on the basis of such formal identities, of a universal concept is assumed to be accomplished by integrating many single sensations. So no immaterial status of the mind is implied. After all, a process (such as knowing) cannot be immaterial, because only material entities can interact.
Signs.
Let us now recapitulate the classification of types of signs and see where signs such as concepts, propositions, or demonstrations, stand in this classification.

A sign is an entity that points to, presents, or represents, another entity.

A  natural sign  points to an(other) entity simply in virtue of what it is as natural being.
So smoke is a natural sign of (the presence of) fire, and the concept 'dog' (not the word 'dog') is a natural sign signifying a mammal that often barks.

A  conventional, or artificial sign,  is one whose significance (i.e. its signifying) comes not from its own nature, but from human convention, such as words, signals, guideposts, etc. There is nothing in the spoken, written, or printed word  ' dog '  (this word) considered simply as a physical fact, that would naturally represent the mentioned animal.

Signs can be either  formal  or  instrumental,  depending on their relation to the knower (a knowing power).

All conventional signs and some natural signs are  instrumental signs.
An instrumental sign, like any other sign, points to some entity (other than it self). But an instrumental sign presents its significatum ( = that what it signifies) to a knowing power only by being first apprehended itself. The smoke is only a sign pointing to a fire, when the knower is explicitly aware of the presence of smoke, that is, of the presence of the sign. One can only know what the guidepost on the road means or signifies by first becoming aware of the guidepost. The word  ' dog '  must be seen before we can come to know what it means.

Some natural signs (and no artificial signs) are  formal signs.  These are signs of which the knowing power need not be aware of in order to know what that sign signifies. Such signs are all concepts, all subject-predicate propositions, and all syllogistic arguments, insofar as they are internalized (that is, not insofar as they are written down or spoken).
Let us continue with concepts, while we know that the same general findings hold for S-P propositions and syllogistic arguments, and while we are not speaking here of the words representing them.
As to this concept itself, it can hardly be said that we are obliged to know it as such and as a concept, before we come to know what it is a concept of. For instance, in the case of the concept of  ' dog ',  one does not first become aware of the concept of  ' dog ',  and only afterward of what the concept signifies. To be sure, one must have the concept  ' dog '  before one can become aware of dog. But still, one does not have to be aware of the concept  ' dog '  in order to be aware of its significatum.
So all concepts, S-P propositions, and syllogistic arguments, insofar as they are internalized in the knowing power and are as such functioning as signs, are  formal signs.  A formal sign is one whose whole nature and being are simply a representing, or a meaning, or a signifying, of something else. In fact they are not things at all, but  relations.  Such signs, in other words, are nothing but meanings or  intentions.  Thus, if one were to ask,  "what is it to be a formal sign?",  the answer would be  "it is simply to be of or about something else."  (See for all this, VEATCH, H., Intentional Logic, 1952, p.12/13 of the 1970 edition).
Formal signs.
It is not hard to see how such formal signs are altogether indispensable to that particular relation of cognitive identity, which is a necessary corollary to a thoroughgoing philosophical realism. For if there are to be signs which would make such a relation of identity possible, those signs could not have definite determinate natures of their own insofar as we consider them in their significative function. If they did have such a nature of their own (as do instrumental signs), then they could represent other things only as being similar to themselves (things signified being similar to these signs), or as causes of themselves (things signified being causes of these signs), or as effects of themselves (things signified being effects of these signs), or as in some way or another related to themselves. But a formal sign does not signify or represent other things in these ways :  It does not present them as they are in relation to it, but rather as those other things are in themselves. The real object, in short, which the formal sign signifies, is itself that sign's very content. Only so can the relation of identity between knowledge and its object come about. The whole nature of a formal sign, in its significative function, consists in  being about  something else. This, then, is what is meant by calling such signs  intentions.
Because of its way of formation, the concept always connects us with aspects of extramental reality, although some such aspects could turn out to be irrelevant, which could, however, be detected later, and which detection process amends the concept. So the concept is objective.
Thus, having said this, we can still say that  having a concept  directly identifies something in us with some aspect or aspects of extramental reality, and in this way we can still say that a concept is a formal sign, despite its empirical way of formation. And it to be a formal sign is indispensable for knowledge to be objective, because a concept is the most basic element of discourse, and that (element) must be intentional. And of course, in addition to formal signs (which is a condition sine qua non [ = absolutely necessary condition, though not necessarily a sufficient condition ] ),  instrumental signs turn out to be very useful indeed for scientific inquiry. However, we cannot do with instrumental signs alone.
Of course formal signs (concepts, internalized propositions and arguments) must be certain higher-level brain patterns (neurological patterns). But in order to know what the concept means, we do not (first) have to be aware of these brain patterns. This is not just an assertion, but an experienced fact.
So, concerning signs :  Words and models are instrumental signs used in science, but they must always be supplemented by formal signs in order to render the knowledge objective.
The distinction of the logical from the real.
Logical entities like concepts, (S-P) propositions, and (syllogistic) arguments, are formal signs, that is, they are intentions, while the extramental things or aspects of them, are not intentions. Extramental things can instrumentally signify other things, but they do not intend them, that is, in signifying they do not involve relations of formal identity. So a given crystal, to take an example, or a number of crystal individuals, can be intended by a logical entity, but they themselves do not intend anything.
The notion of  intention  can be a bit confusing, so we must expound it further.
A given crystal, or a collection of crystals (not as collection, but as individual crystals) is, as has been said, not an intention. Only insofar as it is intended we can call it an intention, namely a first intention. It is then the object of an intention, it is intended, and seen as intended it is an intention. That by which the crystal is immediately intended  is  in fact the crystal-as-intended, and so is also a first intention.
But this first intention can itself be intended -- by a second intention. This means that such a first intention is the object of a second intention (for example when we say that the concept  ' crystal '  is a genus). And because it is the object of a second intention it can also be called a second intention. Again, when a first intention is the object of a second intention it can also be called a second intention, or again in other words, when a first intention is intended by another intention, a second intention, it can also be called a second intention.
It is clear that an object as intended, is itself an intention because it is intended (it is then considered only insofar as it is intended), but it is not an intention when this object cannot by itself intend anything, that is, it is not an intention  insofar  as it cannot intend anything.
On the other hand, a direct object of second intention is a first intention, and insofar this first intention can itself intend something else, it is intended as well as intending. Only an object which cannot intend anything else (while it can be intended) is a real object, that is, an extramental object, and not a logical entity. It is a logical entity only insofar as it is intended (by some logical intention).
Apart from logical intentions, there are other 'beings of reason' such as fictitional 'things', for example the concept of a phoenix.
Second intentions intend first intentions (and only through these, extramental things).  ' Intentions '  in the sense of intending real objects can be considered as  ' intentions in the strict sense ',  while  ' intentions '  intending intentions (first or second) can be called  ' intentions in the broader sense '.
As we have said, real objects are not, and cannot be, logical intentions. This means that even if such an object is a sign, it is not a formal sign. Why? A real object is, in this context, an object such that if it exists at all, it does so independently of being known, independently of getting to be known, that is, independently of any knower or knowing power. So not only are sticks and stones real objects, and are relations like  father of  real objects (real relations), but also mathematical relations, say, the relation of  congruence.  The relation of congruence is what it is (that is, it has certain definite properties) independently of any knowing power. Because of this independence of a knowing power it is not automatically implied by the knowing process, that is, it is not created by and during the process of knowing. The knowing power must direct itself explicitly to it in order to know it. So when such a real object is a sign pointing to something else, it must nevertheless first itself be known. And this means that it is just an instrumental sign. And now we see that all this contrasts sharply with how matters are in the case of formal signs. A formal sign or logical intention, in order for it to (be able to) point to something else, does not need to be itself known first. For knowing things we do not need to know the logical intentions that point to them. Only in Logic we try to find out what these logical intentions are, and attempt to classify them. We know a real thing, or real relation, through a logical intention. The object of our knowledge of real things is not the logical intentions pointing to these things, but those things themselves.
Logic and Metaphysics :  a knowledge of the Logical as dependent on a knowledge of the Real.
Knowledge of the Real depends on the Logical (because the Real is only reached by the application of logical intentions). But knowledge of the Logical depends on knowledge of the Real.
It is not hard to see how a Logic that is thus conceived as being intentional could never be conceived as being self-sufficient and self-justifying. On the contrary, realizing that logical entities are nothing than intentions of the Real ( NOTE 19 ),  the only way such intentions can be understood is in terms of their natural adaptation to the disclosure and intention of the Real. In this sense Logic, so far from being independent of metaphysics or first philosophy, necessarily presupposes it (VEATCH, p.17/18).
Metaphysics is about  what it means  to ask : These three sorts of metaphysical objects are indeed intended by three corresponding sorts of logical intentions : The fact that Logic is, and must be, used in order to understand the subject matter of metaphysics (and, consequently, of science) does not mean, as we saw above, that we have to know the logical tools and instruments (to know the 'logical') before we can come to know the subject matter of metaphysics and of science. The tools are directly used, and there is no need to reflect on them first (for example as to what they are, and in what order they should be used). In the knowing process the right logical tools are automatically applied and applied in the right order. When we do nevertheless reflect on these tools we are doing Logic.
The realistic theory of knowledge, must, as we have seen, be accepted. This means that we know that we can come to know things (ultimately) as they are in themselves, without distortion.
This has a significant bearing on the relationship between Logic and Metaphysics, that is, whether Logic presupposes Metaphysics, or Metaphysics presupposes Logic :  Considering the real to be as it is and what it is, (we can ask)  " What cognitive instruments must apparently have been used in order for one to have attained such a knowledge of the real?"  And to this the answer is :  " They must have been intentions or (equivalently) formal signs of a sort to enable one to get at the 'what', the 'that', and the 'why' of things. It is in this sense, then, that we should wish to maintain that an understanding of the logical presupposes an understanding of the real. Accordingly, a radically intentional Logic will never seek to prove its legitimacy on the basis of the fact that its formulas are in some way tautologous or analytic (always necessarily true), or that they are necessary forms or categories of thought, or that they are somehow eternal and immutable Platonic Forms, or that they are mere arbitrary conventions and postulates which we set up ourselves. The justification of genuinely intentional logical instruments can only lie in the fact that in and through them the real comes to be known without distortion and as it is in itself (VEATCH, p.19/20). But, although sense observations are in principle infallible, the long way of coming to know things in detail cannot avoid errors to creap in. So our knowledge of things, although objective, is not infallible ( NOTE 20 ).
Further elaboration of logical forms.
The Logic which is proposed by VEATCH, and with him by me, differs from mathematical Logic not in the sense that modern formalism as such is defect or inconsistent. It is opposed to the modern formalism in the sense that the latter is irrelevant to Logic when Logic is conceived as an instrument for knowing the real. The difference is between a logic being intentional and a logic that is not intentional.
When considering logical forms one is often liable to interpret them as instrumental signs. Or, having set up a consistent system of logical forms, one can then ask whether they may not be so many signs of similar patterns and relations in extramental reality. In fact, according to VEATCH, the modern mathematical logician is likely to put this very question, by asking whether such logical patterns and relations may not be 'isomorphic' with certain real patterns and relations, or whether they may not be in the nature of uninterpreted formal systems which are susceptible on the one hand of an interpretation in terms of logical relations and on the other hand of one in terms of real relations. However, to consider that so-called logical relations may represent or signify other relations, in virtue of the fact that these latter are like, or similar to, or isomorphic with, the former, is in effect to transform supposedly logical entities from being formal signs into instrumental signs, destroying the possibility of objective knowledge. Any sign, set up in advance, and then interpreting it, makes such a sign instrumental.
The relation of intentional identity.
Sensory cognition, as we have seen, establishes an identity of formal content between the sensory knowing power and sensed object, guaranteeing objective sensory knowledge. But such a knowledge is no more than the awareness of formal contents out there in extramental reality. Genuine knowledge, on the other hand, must consist of the actual relations between these formal contents. So one set of such contents must form a 'togetherness', while another such set must form another 'togetherness', that is to say, a certain set of formal contents must belong to some one thing, while another set must belong to another such thing. By repeated observations or sensory experiences we see that a certain subset of a set of formal contents is repeated over several cases, that is, over several things. So we (the knowers, the observers) begin to get an idea of a class of things, different from another such class. Accordingly, the individual things (members) of one such class have a certain subset of formal contents in common, while they differ with respect to other formal contents. The individual things (members) of another class also have a subset of formal contents in common, but this subset is different from that of the first class. And again, the individuals of this second class of things differ with respect to formal contents not belonging to their common subset of formal contents.
The next diagram symbolizes nine sets of formal contents forming a class of things :

Diagram above :  Nine sets or clusters of formal contents (each such a cluster is, or stands for, an individual thing), forming a class (of things). Each set ( = member of the class, indicated by an elliptic area) consists of (single) formal contents or subsets of formal contents. All these nine sets have one particular subset (red) of formal contents in common. So each of these nine sets can stand for a single individual thing (carrying formal contents), differing from the other eight (single individual things) as regards its pool of formal contents, but (nevertheless) representing a particular species of thing, which is characterized by the common subset (red) of formal contents.
Other clusters might have a different subset of formal contents in common, and so form another class, representing a different species of thing.
The identification (recognition) of persistent clusters of formal contents, as it is done in coming to know things, must be by way of attributing certain formal contents to a certain subset of them, that is, establish them to belong to such a subset, and this is the same as attributing a given formal content to 'something'. This 'something' is not an individual thing as such, but only one insofar as it represents the many clusters of formal contents having some particular subset of them in common, that is, insofar as this thing represents the set of things of the same kind. What is developing here, in fact, is the definition of a particular species of things, that is, the development of a concept. In this way, sensory knowledge is gradually being transformed into rational knowledge. We have just seen that the development of this rational knowledge involves attributions as acts of the knowing power. And these are nothing less than predications, such as  "this thing (already seen as a member of some set) is bounded by flat faces and is blue".  And, in another instance :  "that thing is not bounded by flat faces, but is blue".  After many more observations and comparisons, one sees (in this example) that  "being bounded by flat faces"  is in some way not essential to the class of things under consideration, so it is realized that 'this thing' and 'that thing' mentioned above, are both representing one and the same class. And, little by little the concept of  ' copper sulfate crystal '  emerges or develops  ( Here is meant the five aquous copper sulfate :  CuSO4 . 5H2O ).  And, as one has seen, a host of predications (attributions) are involved. And, finally possessing the concept of  ' copper sulfate crystal ',  one can now point to a single given thing, lying here and now on the table, and say :  "this thing is a copper sulfate crystal",  where now "this thing" is not this thing as representing a particular class of things, but an individual particular thing here and now present. But having examined this particular thing, we are now able to explicitly attribute to it :  'copper sulfate crystal' (even when no crystal faces have been developed in this particular instance). We can also attribute to it other formal contents such as the particular shape as directly observed, but we know that this actual shape does not concur in all other instances of 'copper sulfate crystal' (this is, because the actual shape is determined by extrinsic factors). So we can predicate (the term that stands for) this particular shape only to the particular individual lying before us or at most to a few other such individuals :  We have an instance of accidental predication. This is also the case with 'being bounded by flat faces', because this feature only appears when the crystal happened to develop freely (when it were not allowed to develop freely no faces will develop, but it would still be a [copper sulfate]  crystal).  So while the formation of concepts involves implicit predications, after their formation they can be elements of explicit predications or propositions. And these concepts the basic natural intentional signs or (equivalently) formal signs.

According to VEATCH, p.10, concepts (and also propositions and arguments), if they are to be truly formal signs, that is, entities entirely consisting of just their being intentions, must somehow involve cognitive identity between knower and known. How do they manage to necessarily involve this cognitive identity? VEATCH says that concepts, (S-P) propositions, and (syllogistic) arguments, are logical instruments of such cognitive identity. And through such instruments the relation of cognitive identity between knower and known can come about, that is to say, one can come to know the real itself :  It is made the very content of one's concepts, propositions, and arguments.
But, according to me, to come to know the real itself is already guaranteed by the cognitive identity as it has been set up during sensory perception of formal contents. So there is no need to account for the intentionality of concepts, (S-P) propositions (consisting of concepts), and (syllogistic) arguments (consisting of propositions), by (involving) an additional relation of identity, because we already have such an identity. This additional relation of identity is discussed by VEATCH at p.22-27, and he calls it the relation of intentional identity. This identity is then supposed to consist in identifying a thing to itself (which is a true identity), by first mentally splitting it up into (1)  ' that (it is) '  (in German this is well expressed by Dasein)  and (2)  ' what (it is) '  (in German :  Sosein), and then uniting these again. And this happens in a predication like  ' Socrates is an animal ',  where Socrates is supposed to represent the whole relevant class of things or beings, making the predication equivalent to  ' man is an animal '  ( NOTE 21 ).
The uniting of the Dasein and the Sosein can also take place in a predication, again like  ' Socrates is an animal ',  but now the term  ' Socrates '  being taken to stand for a particular individual, where such a predication is made possible after the concept  ' man '  is known, which latter means that we know that  animality  necessarily belongs to  man  ( NOTE 22 ).
And, according to VEATCH, it is this identity relation of the thing with itself that is the additional relation that is needed to make concepts (and propositions and arguments) intentional.
But we have just seen that (the assumption of) such an additional relation of identity is not necessary. The concepts, and the other logical entities, as they finally have been developed on the basis of repeated sensory experiences and comparisons, are already intentional, and so guarantee objective knowledge (where "objective knowledge" does not necessarily mean "true knowledge").  However, we do not need to abandon this additional relation. It could be just the effect, or result, of the mentioned repeated sensory experiences and comparisons. All the initial attributions of formal contents and the subsequent negations of attributing certain particular formal contents with respect to some given 'center of attribution', lead to  per se  attributions, or  per accidens  attributions ( = attribution with qualification), or  negated  attributions (negated without qualification), which in turn lead to genuine concepts, each of them consisting solely of the relation of identity, that is, after having mentally split up the thing into its Dasein and Sosein, the concept consists in uniting them again. And this results in a knowledge that is supplemental to just sensory knowledge, a knowledge that we can call rational knowledge.
Seen in this way, there is sufficient evidence that such a relation of identity (as a result of processing a multitude of sensory knowledge) is a thoroughly intentional relation. Indeed, to finally recognize a thing in terms of what it is, is to recognize  it  (and thus to intend it). And thus to relate by identity an  "it"  to its  "what"  (which is recognizing the thing) is simply to intend or know this  "it".

So, initially only having internalized a mozaic of formal contents (features), finally develops into recognizing  things  among which these formal contents are distributed, resulting in the formation of concepts, each one of them exclusively consisting of a particular relation of identity.
So our only difference (in view) with VEATCH is that while he sees the relation of identity as it is present in concepts (propositions and arguments) as a condition for cognitive identity,  we see the relation of cognitive identity as the condition for finally realizing the relation of identity between the thing and its whatness (as described above). The resulting concept is a true intention or (equivalently) a true formal sign.

We have discussed concepts (and concomitantly, propositions and arguments), and stated that they are genuine logical entities, logical intentions. But what, precisely, is their ontological status? Well, because they are intentional relations (of identity), they are not ordinary relations, that is, they are not real relations, not real things :  Real things and real relations are not each for themselves divided into an  'it'  and a  'what'  (and then united again),  so logical intentions (which are each of them so divided [and united again] )  are called  beings of reason  (entia rationis). But what exactly is a being of reason? Is it something that exists immaterially? To answer this question, we first consider the following thesis, which is, I deem, supported by experience :

Every existing entity is penultimately based on physical matter (which itself is based on prime matter).

For our problem this means that even 'beings of reason' must penultimately be based on physical matter. To be more specific, a given concept (which is a being of reason) must correspond to some neurological pattern (probably a highly dynamic one) in the brain. At this level, the neuron level, that is, the level of the brain cells, we do not, however, see the content of the concept. How can this be? For this to understand, we should go back to our earlier exposition about the more or less gradual development of the content of a concept. We had found out that this content is the result of integrating decoded information, information that came in, in an encoded form, during sensory experience. The formed content of the concept is then stored in the brain as a result of udating earlier versions of the content. When explaining the encoding-decoding process we had used the analogy of a grammophone. And we could use the same analogy in explaining in what way the formed and stored content of a concept exists in the brain. We will, however use a slightly different, but equivalent, analogy just for the sake of clarity and flavor.
When we inspect a DVD (digital video-audio disc) which contains a movie, for instance by looking at the disc through a magnifying glass or microscope, we do not see the movie. What we see looks like a code or something. And indeed, when we decode this code with an appropriate decoding device (reading device, DVD player, plus monitor) we see the movie. So we would be inclined to call the DVD the 'matter' and the movie the 'form'. And because the DVD material, even when the movie is not yet recorded on it, possesses already content (it is a material of a certain kind, different from other materials), we cannot see it, of course, as prime matter, but as a physical thing. The movie must then be an accidental determination of that thing. But this cannot be, because we can have several DVD discs consisting of the same material, but with different surface structures as a result of them containing different movies. So the accidental determination of the disc ( NOTE 23 )  is not the movie, but the surface structure which embodies the coding (like the groove of a grammophone record). The movie only appears after the code has been properly decoded. So when we say that the movie is on the DVD, it is as such no more than a 'being of reason' (in the present case [analogy], although a being of reason, it is not an intention, but an instrumental sign [it purports to be something that is similar to the real thing] ).
In the same way we can think of a concept (which is a being of reason) :  A concept is, like the movie, carried by a material substrate :  a physical brain pattern, a neurological wiring pattern (the 'groove' of the brain), but one should immediately realize that the concept is not this brain pattern. Therefore this brain pattern does not reveal the content of the concept. It is just an accidental determination of the brain, and with it of the human body having this brain. Only after this brain pattern has been decoded properly, the content of the concept is revealed. So only in this sense we can call a concept a being of reason.

Let us continue with the relation of identity.
A thing can be mentally divided into an 'it' and a 'what', and this 'what' can be what the thing essentially is. In this case the relation of identity is clear, as we saw above.
The identity is less clear in the case of  ' Socrates is tanned ',  because being tanned is not what Socrates essentially is (evident from the fact that he is not always tanned). And especially this case, in which the identity is less clear, demonstrates the difference between a logical relation, here a subject-predicate relation, and a real relation :  The logical relation is expressed as an identity :    ' Socrates  is  tanned ',  while in reality Socrates is not identical to (being) tanned, that is, there is no formal content, as signified by the terms that is commonly possessed by Socrates and (being) tanned.  Socrates  and  (being) tanned  are just accidentally connected.
More generally :  A relation of subject to predicate is never the same as, or even similar to, a relation of substance to accident. Instead, it is always a relation of logical identity, S is P.  But clearly, a substance could never be related to its accident in this way :  for if a substance simply were its accident just as such, it would not be itself (but something else, namely its accident), it would not be a substance (VEATCH, p.38). So the very structure of a predication generally is different from the structure of that segment of extramental reality which that predication is supposed to signify ( NOTE 24 ).
The same is the case with a concept.
A concept might well be the concept of a relation -- e.g., a concept of  " father of "  or "congruent to".  Yet merely because a given concept happens to be a concept of a relation (there are other concepts which are not concepts of relations) certainly does not mean that the concept just as such has to have the same structure as the relation which it represents. For instance, the concept of  ' father of '  is, like any concept, a universal, and as such it is but a relation of identity between an abstracted (the encoded being decoded) formal content and the particulars of which it may be predicated :  Peter is the father of Paul (here the relation " father of " is specified further as to become the relation " father of Paul ").  In other words, the structure of the concept is not one involving, to stick with our example, the relation of father to child, but rather the relation of logical identity. True, the concept may represent the relation of father to child, still its own relational structure  is  the logical relation of identity, and not the relation of father to child. Thus the structure of the concept (not its content) is the same, no matter what the concept may happen to be a concept of. Likewise, the structure of the proposition, according to which a thing is identified with its own 'what' (also when this 'what' is only  per accidens), would scarcely have to vary with the thing the proposition was about or with what could be said about that thing. And so also for arguments (demonstration) as well (VEATCH, p.38/9).
In mathematical Logic there is no distinction being made between intentional and non-intentional forms. All signs are supposed to be instrumental. The point in distinguishing between intentional and non-intentional forms is that since the former have supposedly a properly intentional structure, one is able through them to come to know any thing whatever, no matter what that thing's form or structure might happen to be. In contrast, no sooner does one either exclude or ignore (as in mathematical Logic) such entities as formal signs, than one must also deny that there are any common intentional forms and structures which can serve as instruments (not as instrumental signs) through which all other forms and structures can come to be known. Instead, there must be just as many logical forms and structures as there are real forms and structures. Indeed, considered purely formally and structurally, there would be no way of distinguishing the latter from the former. The real, in short, becomes simply confounded with the logical (VEATCH, p.39).
So the structure of a logical entity (concept, [S-P] proposition, and [syllogistic] argument) is not necessarily the same as the structure of the fact which is signified by that logical entity. In mathematical Logic they do have the same structure.
Introductory discussion of propositions.
Mathematical Logic holds that all propositions express relations. It classifies them into types : Indeed there is nothing wrong with such classifying. However, mathematical logicians do not distinguish between logical relations and real relations. All three mentioned relations are real relations, and each one of them can be intended, that is, can be known. By what can they be intended? By a logical intention. And by what logical intention? Well, by nothing else than some subject-predicate relation.
Indeed, by intending a given real relation by a subject-predicate relation is equivalent to say  what it is, that is, what the given real relation is. For example the relation  teacher of  is :  Someone who passes on knowledge (to someone else).
Further, the real relation  teacher of Plato  is :  Someone who passes on knowledge to Plato.  But, sticking with just the relation  teacher of,  we can say :

This (relation) is a passing on of knowledge,

and this is a genuine subject-predicate relation (S-P relation), and is thus a relation of (logical) identity (expressing what the [real] relation of  teacher of  is ) :
First we mentally separate the 'thing' (which here is the relation  teacher of  [which itself belongs to a particular type of being] )  from  'what it is'  (which here is :  a passing on of knowledge), and then we re-identify again :

This (relation)  IS  a passing on of knowledge,

where we can also say :

The relation  teacher of  IS  a passing on of knowledge.

Because a relation as such is abstract, resulting in the subject term being abstract, the predicate must, in order to be identified with the subject, be abstract too, and this is indeed the case :  the term  ' a passing on of knowledge '  is abstract.

When instead of a relation (which is just an auxiliary being), a genuine thing or being, say, Socrates, were designated by the subject term, this subject term is concrete, and so the assigned predicate term must also be concrete. That's why we do not say :  Socrates is humanity,  but  Socrates is human.  Here  ' human '  signifies  humanity,  but connotes any individual having this  humanity,  so the term  ' human '  stands for concrete wholes, that is for all individuals having  humanity.  And now the term  ' Socrates ',  which is the subject of our proposition, restricts all these individuals to one only, namely Socrates. Consequently,   ' Socrates '  and  ' human '  designate the same, and can be identified, resulting in the subject-predicate proposition  ' Socrates is human '.

So now we have shown, by means of an example, that real relations can come to be known by intending them by subject-predicate propositions, which are intentional relations of identity.

The real relation  Socrates was (is) a teacher of Plato  can, in addition to being studied as regards to what  ' teacher of '  means, also being studied as regards to what Socrates is, either essentially or accidentally. His being a teacher of Plato is, with respect to him being human, accidental, and we could study this accidental determination of him. In order to know this determination, it must be intended. By what? By a logical intention, which as such is a logical relation (of identity). This intention is :

While  Socrates-being-at-the-time-the-teacher-of-Plato  is a unity (albeit accidental), we mentally first separate  ' Socrates '  from  ' the teacher of Plato ',  and then re-identify them again :

Socrates  was  the teacher of Plato.

So this subject-predicate relation of identity intends the real relation of  teacher of.  This real relation consists of  Socrates  and  Plato  being related to each other (in the given order) by   is teacher of   (which latter is the relation proper) :

while the intending logical relation consists of subject (  ' Socrates ' ),  copula (  ' was ' ),  and  predicate (  ' the teacher of Plato ' ). See first diagram .

The intending of our real relation by a logical relation can be represented by combining the two diagrams :

The inserted notion  was  makes the relation between Socrates and Plato being asserted, and indicates that the assertion refers to the past.
Above we had a case of a real relation to be intended by a logical relation, where, however, the corresponding verbal expressions were identical. But, we know that despite this verbal identity of these expressions they are nevertheless fundamentally different :  The expression taken as a two-term relationship is an instrumental sign. It points to something in extramental reality (or in that which can be held for this reality), that is to say, it points to a fact, that is similar, or at least similarly structured :  two real entities really related to each other. Only when the expression is taken as a one-term relationship (that is, as a subject-predicate proposition) it is a formal sign. So the two forms of the expression are fundamentally different from each other :
The one is real, and is an instrumental sign. It can be intended. It cannot itself intend anything (because it is just an instrumental sign).
The other is logical, and is a formal sign. It can be intended, and can itself intend something else.

Apart from the above described case of verbal identity between intending and intended relation, there are other cases where the verbal form of the intending relation differs from that of the intended relation. To investigate such cases we can ask :
What exactly in extramental reality is being signified by propositions like

Socrates is human, and

Socrates is tanned ?

Well, what is signified by these one-term relations is the fact that Socrates has humanity, and, respectively, has tan.
These two facts can respectively be pointed to by the following instrumental signs, which are two-term relations :

Socrates has humanity.   The two terms, viz.,  ' Socrates '  [referring to supposit]  and  ' humanity '  [referring to the Essence] are related to each other by way of the second [term] being (essentially) 'had' or 'possessed' by the first [term]. As such, i.e. as a mental (cognitive) state, it points to a pattern in extramental reality (a fact) that is structurally similar to it ( NOTE 25 ).

Socrates has tan   The two terms, viz.,  ' Socrates '  [referring to a substantial being]  and  ' tan '  [referring to an auxiliary being] are related to each other by way of the second [term] being (accidentally) 'had' or 'possessed' by the first [term]. As such, i.e. as a mental (cognitive) state, it points to a pattern in extramental reality (a fact) that is structurally similar to it.

The fact  Socrates has humanity   is  intended (not just pointed to by an image) by the subject-predicate relation  Socrates is human, which is a formal sign.
The fact  Socrates has tan   is  intended (not just pointed to by an image) by the subject-predicate relation  Socrates is tanned, which is a formal sign.
Above we spoke about the fact (namely a relation) described by the proposition  ' Socrates was the teacher of Plato ',  which (proposition) is a two-term relation, and we discussed how it is or can be truly intended. We found that it could be intended by a one-term relation which is verbally the same as the corresponding two-term relation.
However, there is yet another way by which the relation  (Socrates was) the teacher of (Plato)  can be intended.
Socrates-being-(at the time)-the-teacher-of-Plato  is itself a complex unity really existing (at the time), which we can subsume under :  unities of order.
Well, in order to come to know such a unity of order, we can take this unity as the subject of the intending subject-predicate proposition. That is, the predicate then expresses what this (particular) unity of order is, which in turn means that the S-P proposition asserts what this particular unity is :

This unity of order  is  Socrates being (at the time) related to Plato by the relation of  teacher of.

Here,  "this unity of order"  is the subject term, while  "Socrates being (at the time) related to Plato by the relation of  teacher of "  is the predicate term.
Accordingly :
As to intending the real relation between  substance and accident (such as in Socrates was the teacher of Plato) :  This  real  relation, which is not a relation of identity (because the real Socrates is not identical to his being the teacher of Plato, i.e. he is not identical to his replaceable determination), but one of  inhering  (a given formal content is inhering in a substrate), this real relation is intended by the  logical  relation of  subject and predicate  (like all real relations are so intended), and this latter relation is a relation of identity, and thus an intentional relation, and not a real relation.

Let us now further discuss the difference between instrumental and formal signs.
Propositions like

Socrates was the teacher of Plato, or

Socrates was earlier than Aristotle,

are, as real relations, two-term relations. They can be intended by corresponding one-term relations, which are subject-predicate relations and therefore logical relations, in two ways, as we have seen earlier :

Of course the words (as words) in these propositions are conventional signs. They must first be known (that is, be aware of, explicitly read) before we get their significatum to be presented in our mind (reading or hearing the words evokes the corresponding mental state). So the proposition, as a sequence of words (when read or heard), refers first of all to a corresponding mental state, and this state then in turn intends a fact in extramental reality as soon as this state is in the form of one of the above two versions of the intending logical relation. If, on the other hand, this mental state has the form of a two-term (or many-term) relation, then it is just an image of the extramental fact and thus only an instrumental sign.

Now consider the proposition :

Socrates is tanned.

This is a one-term relation. And also here the words are conventional signs. So the proposition, as a sequence of words, refers first of all to a corresponding mental state. This mental state cannot, however, be an image of the extramental fact, because in reality Socrates is not (identical to) tanned. So it is directly a formal sign, and cannot be an instrumental sign. Accordingly, the mental state  Socrates is tanned  is a logical relation of identity (expressed by "is"), and as such a formal sign pointing to the fact that Socrates has tan.

The identification of predicate with subject in a proposition is but a development of the relation of identity in a concept. Moreover, just as intentionality is served by a relation of identity in the case of the concept, so also it is served by the identification of predicate with subject in a proposition :  that is to say, it is by such identity and only thereby, that we come to know, or cognitively intend, what a thing is.

The upshot of all this is that all propositions that want to be logical or intentional forms must be subject-predicate propositions. All other propositions are not intentional.

The transformation of  ' Socrates was earlier than Aristotle '  as a two-term relation (and likewise all other two-term relations),  into  ' Socrates '  ( = subject),  ' was '  ( = copula), and  ' earlier than Aristotle '  ( = predicate), which is a one-term relation,  takes place by approaching  ' Socrates '  and  ' earlier than Aristotle '  by a second intention, namely by saying that  ' Socrates '  is the subject, and  ' earlier than Aristotle '  the predicate. This is not a mere reduction of the two-term relation to a one-term relation (subject-predicate relation), but a sort of 'meta-intention'. When we want to know about something we thus must use the subject-predicate (S-P) propositional form. And we want to know either about one or another determination, like  ' earlier than '  or  ' teacher of ',  or (we want to know about) a given individual, such as Socrates. In both cases we must use predicates that will describe the determination or the individual. So if we want to know about an individual, say, Socrates, concentrating now on this case, the only way one can do so is to use predicates that will describe Socrates, and that will be related to the subject  ' Socrates '  by a relation of identity. This will be true even if a given predicate signifies some accident, for example a relation that relates Socrates to someone else, say, the relation of being earlier than Aristotle, or of being the teacher of Plato. Nevertheless, to identify  ' teacher of Plato '  with  ' Socrates '  does not mean that one is identifying the real relation as such with Socrates. After all, one does not say  ' Socrates is (or was) the relation TEACHER OF PLATO ',  or, equivalently,  ' Socrates is (or was) teacherness, or teachership of Plato '.  Nor does such identification of predicate with subject mean that one is reducing the real relation of Socrates to Plato to a mere subject-predicate relationship. On the contrary, Socrates is (or was) really and in fact related to Plato (in the sense of 'happened to be related to Plato) as his teacher. And as such this is a two-term relationship, not a one-term relation (S-P relation). However, the fact of this relation we human knowers come to know and understand through an entirely different relation, viz., the intentional relation of identity between subject and predicate, which is not a relation between Socrates and Plato, but between  ' Socrates '  as subject and  ' teacher of Plato '  as predicate.

In the same way (now in the domain of mathematics) we can say :
Concepts, propositions, arguments, knowledge, and intentional Logic.
It is the  proposition  that is central to intentional Logic :  The proposition presupposes concepts, which are intentional formal signs of  the  what  of things (s.l.). The proposition is not merely composed of concepts, but connects them in order to intend existence of states of things. And propositions are themselves connected to form arguments that intend causal structures in objective reality ('causal' in the broadest sense), that is, they intend the  why  of states of things.
But as a genuine intentional proposition, the proposition must be a subject-predicate proposition, which is a genuine logical intention of identity. This we can argue along the following lines :
  1. The genuine logical proposition is a (natural) sign, not an instrumental sign, but a formal sign, as demanded by a realistic view of knowledge. As such it is a being of reason, not a real being or relation. The states of affairs in the intending mind are different from the intended things, features or states, which is evident from the fact that, for instance, a real relation such as 'longer than' can never be present as such in the mind.

  2. The sign intends.

  3. Intending = knowing, resulting in knowledge.

  4. Knowledge is first of all :  what a given something is.

  5. A concept already implicitly contains (the answer to) what a given something is.

  6. A proposition explicitly expresses what a given something is, and also that it is (and an argument explicitly expresses why it is what it is).

  7. From this it follows that the logical intention with respect to a proposition must be an  IS-proposition (or some other tense of the verb 'to be' in order to refer to time) (what something IS), from which in turn follows that it must be a subject-predicate proposition (S is P).
This concludes our discussion about the necessary conditions for accepting an Intentional Logic as first proposed by VEATCH in 1952. We have come to accept these conditions.
The next document will systematically expound Intentional Logic.
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