www.TheLogician.net © Avi Sion - all rights reserved
© Avi Sion
All rights reserved
© Avi Sion, 2003. All rights reserved.
In the present chapter, we shall try and clarify the processes of conceptualization, i.e. how we develop abstract ideas from the data of experience. Many philosophers have previously attempted this difficult task, but have strayed into error or irrelevancy due to their failure to grasp all the logical issues involved. We need to explain how comparisons and contrasts are effected, without engaging in circular reasoning. We need to show that logical tests are not arbitrary standards, as some accuse, but constitute the only honest and sane way to assess any data input. We need to clarify verbalization, and ensure that it does not skew our ideas. We may also try and propose a theory of ‘universals.’
Alleged apprehensions of sameness and difference are the primordial basis of all concept-formation, that is of grouping and naming or classification. These are of two kinds, particular sameness or difference, which relate to purely perceptual (material or mental) or intuitive (self-known) items; and later abstract sameness or difference, which relate to conceptual products of the former. Or we could say more precisely, sameness and difference on a particular level are the foundations of abstraction, i.e. whatever we judge same to each other and different from other things become thereby members of the first abstracts, all others being ultimately derived from them.
An important insight or principle we may suggest at the outset is that similarity is not something we apprehend – it is dissimilarity we apprehend; similarity is just the absence of dissimilarity. Thus, despite the polarities we have given the words, similarity is something negative, whereas dissimilarity is something positive. Everything seems the same to us, till we discern some difference. We judge things singular or same, if we have noticed no plurality or difference between them. Thus, strictly speaking, dissimilarity can be experienced, whereas similarity is a rational object.
Let us first consider certain percepts (material or mental objects of perception) in the visual field (specifically, shapes), and then we shall turn to other visual percepts, as well as auditory percepts and those in other sense-modalities.
When faced with two visible material percepts (phenomena appearing at the same time in the visual field), we ‘compare’ them mainly by mentally projecting (externally imagining) parallel lines from points on the one to points on the other (the points being imagined subdivisions of the phenomena, into light or dark dots – digital 1s and 0s). If all such lines pair-off dots which are both alight or both dark, the objects are judged to be completely similar (identical); if no dots thus correspond, the objects are judged completely different, if only some correspond, the objects are judged in some respects same (similar) and in other respects different (dissimilar). There are thus degrees of sameness or difference.
Such comparison (in its widest sense, including both comparison with the positive aim of finding points of similarity and that with the negative aim of finding points of dissimilarity, i.e. ‘contrast’) thus involves an imaginative act (specifically, a hallucination of mental lines into the material region of space), but its result is given by the visual phenomenon (there evidently are or are not pairs of light or dark dots at the two ends of the lines).
Another, less direct way we compare visual material objects is by externally projecting a mental image of one object (usually one perceived previously, whose image is thus stored in memory) onto the other material object (currently present in the visual field). Such juxtaposition primarily occurs when the two material objects are not simultaneously present, or so far apart in space that focusing on one turns one’s attention away from the other so that they cannot strictly be regarded as sharing the same visual field at the same time. In such case, we overlay an image of one object on the other, and consider and count how many dots cover each other over and how many do not. Here again, an imaginative act is involved (projection into external space of a mental image or memory), but the judgment is based on passive observations.
A third, still less direct way is to compare and contrast mental images of both the material objects under scrutiny – this may be used for instance if neither object is present long enough, both being too ephemeral. Other ways are experimental: the observer may seemingly move himself relative to the two objects so that they are in the same line of vision (appeal to perspective) or seemingly move one object so that it is physically on top of the other and blanks it out in every direction. Such physical experiments do not per se involve mental projections.
In practice, all these various ways might be used in combinations, reinforcing each other or mitigating our judgments somewhat (as to the degree of similarity and dissimilarity). Physical experiments may be criticized as actually changing the visual field, in that what is compared after said movement is not the original scene, but a new scene – in which case, we have to in fact appeal to a memory (i.e. a mental image) of the object moved, juxtaposed on its alleged new manifestation, and judge the two as the same by an inference (image 1 is like object 1 and like/unlike object 2, therefore objects 1 & 2 are like/unlike). Therefore, even such experimental comparisons involve imagination.
In addition to comparisons of shape, we must consider comparisons of size – that is, the measures or degrees of things. Two things may have the same shape, but different sizes. To deal with this problem, we introduce the concept of proportion. Comparative measurement is an experimental act in that, in imagination or physically, we bring to bear a standard of measurement, a graduated measuring rod. In visual imagination this simply means that, instead of comparing dots (as above), we compare collections of dots – dashes (lines of two or more points), while ignoring or making note of the differences in their numbers of constituent dots (according as we are satisfied with imprecise proportions or need to be exact).
Considerations of ‘scale’ often involve a mental act of ‘zooming in.’ In Buddhist Illogic, I state:
the zooming in is merely production of a new image – so we are not even, in
fact, repeatedly subdividing the same image; we merely say ‘suppose
this image is a detail of the preceding’. The new image has the same size as
the preceding, but its scale is declared different.
It is worth stressing here that this declaration need not be verbal, and is more precisely an intention. That is, we intend some visualized line to be considered as a portion of another visualized line, even though both lines are in fact (about) the same size when projected in our heads. Neither the mental projection of images, nor a verbal declaration, can fully explain ‘proportion’ – we additionally must, note well, refer to the intuited intention that this line ‘represents’ a fraction of that line. Thereafter, we can specify how many such fractions would equal the whole.
The mental drawing of lines first mentioned may also be criticized as taking time and involving shifts of attention, so that by the time the lines are drawn it is no longer the original two objects that we are comparing but our many mental images (memories) of them. However, these various images have each in succession passed the test of correspondence with their original objects (image 1 matches object 1, image 2 matches object 2) – we express this fact by calling them ‘representative’ – so that we may justly infer the resulting judgment (that objects 1 & 2 are the same/different) from the equality or inequality of their images. In conclusion, the comparison and contrast of material objects may well generally involve mental projection of images of their objects, though many rely mainly on projection of lines between objects too.
It should be mentioned that visual experiences do not only involve shapes, but also light-intensity (shadings) and frequency (colors). How for instance do we recognize various colors as all green, say, although they range noticeably? For such qualities, an argument by analogy seems called for. It is also by analogy that we must here try to explain comparisons with respect to the experiential fields of the other sense-modalities, sounds, smells, tastes and touch phenomena. Presumably, we mentally cut up the experiences into elementary phenomena, which we then compare to each other or to imaginary substitutes, or experimentally determine in some way (e.g. at later stages in development, we could record sounds into a computer and have it project on its screen visible waves which mathematically correspond to the sound waves concerned).
Whereas material phenomena of light or sound have obvious mental equivalents – we can think visual images (including colors) or speak to oneself (i.e. in one’s head) at will – it is not immediately evident that we can produce mental images (memories) of smell, taste and touch phenomena at will while awake (though my own introspections suggest they do occur in dreams while asleep). Be that as it may, unless we can think up some fitting alternative theoretical scenario, we have to assume the doctrine that imagination (or at least memory) of these sense-modalities is possible, since we evidently are able to recognize such phenomena!
We should also consider comparison of mental objects of perception. With regard to the visual field, first, internal or external imagination of lines, joined at will from point to point of any two objects, would be a sufficient hypothesis. There is no logical need, here, to produce a mental image of either mental image, since just as soon as the primary mental objects are thought of (with a view to compare them) they are present in the mental visual field and such imagination would be redundant. But one can, rather than mentally draw lines between them, mentally move one mental object over to the other, juxtaposing them for point-by-point confirmation of similarity or difference. Such moving seemingly does not require further confirmation by images, since it is as it were guaranteed by the observer’s introspected will. Similarly supposedly for the other sense-modalities.
Comparisons and contrasts between intuited particulars, on the basis of which abstracts concerning the psyche are assumed, are more difficult to trace. They evidently occur introspectively somehow, but I cannot at this stage suggest just how, so I will leave the issue wide open.
The above-mentioned first abstracts are only among the most basic. From their application a whole world of more specific or generic abstracts is gradually inferred, adduced or assumed. For example, there are also, we assume by analogy from phenomenal and intuitive feelings, ‘abstract feelings’ inferred from the value judgments and behavior patterns of the observer. These are not to be confused with pleasure/pain sentiments (which are physiological phenomena, i.e. concrete material phenomena experienced within the body), which may occasionally be caused (we believe) by abstract feelings. Nor should we confuse these with what I have earlier named ‘mental feelings’ (if any such exist) and ‘intuitive feelings’ (which are raw data for abstraction). Abstract feelings are hypothetical entities, stretching terms by analogy; they are more judgmental, or rational in nature.
With regard to cognition of more abstract sameness or difference, then, we should in principle regard our identifications as hypotheses subject to the laws of adduction. The concepts of concrete sameness and difference are by analogy extended to include presumed/alleged/postulated abstract sameness and difference. We do not directly ‘see’ abstracts as same or different, as we do concretes. Rather, we postulate that something akin to sameness or difference relates two given abstracts (respectively inferred as above described), and then test this theory by adductively confirming or rejecting it, in competition with conceivable alternatives. The process of comparison is here less direct, and less permanently sure in its results.
In practice, the objects we compare are rarely simple visual shapes, but complexes with many aspects. All the above-described concrete processes, and additionally many abstract ones, will be called upon in tandem for any given act of comparison. So it is difficult to describe comparison in a succinct manner. For instance, let us compare two carpets on my living room floor. I can basically relate them in respect of their rectangularity by drawing lines from the corners of the one to those of the other. This is possible even if they are different in size or differently placed, by calling on perspective adjustments. But if one were round and the other square, this would be inconclusive, and I would have to refer to their color or texture (a touch phenomenon), or more abstractly to their fabric (wool or cotton) or even their function (warmth, decoration, etc.). Or comparing two trees, I would not expect their overall shape to be always similar, but would refer instead to bark and leaves, or cells viewed under a microscope, or more abstractly to observed biological processes (themselves complex).
In conclusion, sameness or difference are geometrical judgments at the simplest concrete level of visible shape, but at more complex levels, other sense-modalities as well as abstract hypotheses and inferences (themselves somewhat based on previous concrete experiences) are generally taken into consideration in determining sameness and difference. Nevertheless, I have attempted here to postulate a scenario, which would credibly explain how we apprehend sameness or difference, already to some extent, at the simplest concrete level. I personally see no alternative explanation yet, and so regard it as a good working hypothesis, justifying our comparisons (to the extent that we have been attentive enough, of course). It is acknowledged, however, that even apparently simple cases are usually far more complex in fact, and it is difficult to describe such processes precisely, as they vary tremendously (involving many sense-modalities, and conceptual/logical work too).
Direct or indirect comparison/contrast may be considered as principles of logic, insofar as it is on their basis that we begin conceptualization. Once percepts of any kind are thus declared same or different in certain or all respects, we mentally group their images in our minds (probably more precisely, link their memories in the networks of our brains) and, usually but not always, label them with a name (i.e. a physical or imaginary sound – and in the case of written language, a visual symbol). The value or utility of naming is that it provides us with an easily invoked substitute for experiences difficult to bring to mind (like smells, tastes or touch phenomena) or more abstract concepts.
It must be emphasized that the mystery of sameness and difference cannot (as some philosophers have tried) be explained-away by just saying that the arbitrary names we give to things are their only common grounds. Logically, this hypothesis begs the question, in that names too have individual instances, which must be judged same or different!
The prime concepts resulting from such grouping and naming (effectively these are propositions, like ‘x is same to y, therefore both shall be symbolized by z’) may then serve as objects in eventual derivative ‘abstract’ comparisons, which in turn may yield more abstract ones still, as classification progresses higher or deeper. It should be clear, at least if the above explanations are naturally convincing, that the role of imagination in comparison processes does not detract from the objectivity of the sameness or difference concluded. The mental projections involved do not affect the material objects they try to represent (and are shown to do so by matching) – they are not ‘mind over matter’ type volitions, arbitrary manipulations – they are merely juxtaposed. For this reason, we can fairly regard our prime concepts (and their eventual derivatives by inductive logic) as ‘empirically’ based and epistemologically justified.
Allied to sameness and difference are the concepts of compatibility or incompatibility, which underlie what Aristotle has called the three ‘laws of thought’ – identity, non-contradiction and exclusion-of-the-middle. How do we apprehend things (percepts, intuitions, concepts and propositions about them) as able to coexist (compatible) or as unable to do so (incompatible) or problematic (not established as either compatible or incompatible)? We must answer this question urgently, if we admit that these logical processes of confrontation (or facing-off) are as basic as those of identifying sameness or difference. The whole of logical science is built on their assumption, and we must explain how we know two things to be harmonious or mutually exclusive or of undecided correlation.
An important insight or principle we may suggest at the outset is that consistency is not something we apprehend – it is inconsistency we apprehend; consistency is just the absence of inconsistency. Thus, despite the polarities we have given the words, compatibility is something negative, whereas incompatibility is something positive. Everything seems harmonious to us, till we discern some conflict. We judge things consistent, so long as we have no logical insight of inconsistency between them. Thus, strictly speaking, inconsistency can be directly ‘seen’, whereas consistency is normally assumed till found lacking. In some cases, consistency is indirectly put in doubt, without some direct inconsistency having been found, so that an uncertainty arises.
Aristotle formulated his three ‘laws’ firstly with reference to percepts or concepts by stating them as ‘A is A’, ‘A cannot be non-A’ and ‘Either A or non-A’. In a later stage, they are formulated with reference to propositions. As I argue extensively in Future Logic, these laws are not laws in the sense of a-priori principles or arbitrary axioms, as some have claimed, though they are self-evident in that to deny them is self-contradictory, but have to be regarded as given in their objects somehow. Psychologically, they are profound impulses (which may be ignored or followed), which make humans rational; ethically (in the ethics of knowledge gathering), they are indispensable tools and imperatives to actively respond to certain epistemic situations in certain ways (though one can be dishonest or unaware and ignore the facts, or evasive or lazy and ignore the imperative).
Identity brings to mind the visual image and sensation of calm or attraction or a tendency to merge of two things (equation), contradiction that of conflict or repulsion or explosive collision between them (because they cannot occupy the same place), while exclusion of the middle refers to a gap or deficiency between them (raising doubts and awakening questions). These may be imaginative representations for philosophical discussion like here, but they are not always (if ever) involved in concrete identification of identity, contradiction or research needs. Their involvement is more technical or abstract, straddling as it were the experiential domain and the conceptual knowledge domain. Although formulated as a triad, the laws of thought are three aspects of essentially one and the same necessity.
The law of identity, simply put, tells us “what you see is what you get” – it is a mere acknowledgment that the data of phenomenal experience are the fundamental givens of any knowledge enterprise; that there is ultimately no other data to base inference on, so that all their details must be paid attention to and taken into consideration in any inference. With respect to its formulation as ‘A is A’, with reference to terms rather than propositions, this law would simply mean that, if we for instance compare the constituent points in any two material or mental complex phenomena, we have to acknowledge that wherever dots appear (or fail to appear) to us, we can definitively say that there are (or are not, respectively) dots (at least phenomenal dots) – at least for now, until if ever the situation changes or further scrutiny tends to belie the first observation (because many later observations supplant the first, by their statistical weight).
Identity is a law, because there is no other way to conceive things – at this phenomenal level to ‘seem’ is to ‘be’. You can deny your phenomenon’s reality, but not its very occurrence or existence. If you try to deny your actual phenomenon by immediately hypothesizing some invisible conflicting ‘phenomenon’ behind it (a noumenon, to use Kant’s word), you are condemned to being basically unempirical and therefore without epistemological justification for your own act. You have nothing to show for your case, since by definition you appeal to the unseen, whereas you must acknowledge the seen as seen to at all deny it. The baselessness and circularity of such refusal to accept the phenomenon (as a phenomenon, no more, at least) merely reflects that the phenomenon experienced is the given to deal with in the first place (for this reason any denial of it is bound to admit it, implicitly and explicitly by referring to it). All such argumentation is of course very conceptual, and so only at best lately and peripherally significant in any actual act of acceptance of the phenomenon as such.
Phenomenologically, the law of identity means that an image of a material entity, mentally projected externally onto that entity, does not blank out the entity (being as it were in a parallel space, transparent). When such mental image seemingly shares outer space with the material body it is projected on, then the phenomenon as a whole has changed, though the material entity stays on (perseveres as an appearance), having been augmented in respect of a mental image. That is, the new phenomenon is enlarged (by an additional image) in comparison to the originally given phenomenon. This means that postulation of a noumenon merely adds a mental component (including additional phenomena) to the first presented phenomenon, and does not succeed in erasing the first phenomenon, precisely because it is introduced in relation to the first phenomenon (specifically, as an attempt to explain it or explain it away).
The law of identity is an impulse, a call to empiricism, which we normally obey without doubt or question. It acknowledges that appearances might in the long run change or prove misleading, taking into consideration all other appearances. It does not deny, nor accept ab initio, that behind the seen appearance there might be unseen or invisible events or things; but such outcome can only be arrived at through an overall consideration of all experiences and much pondering. That is, ‘noumena’ might well exist beyond a given field of phenomena – but they would have to be end products of an evaluative process and could not be first assumptions. Since evoking noumena does not in itself annul phenomena (merely adding more phenomena to them), the questions inherent in phenomena and their apparition to us remain unanswered.
The reason why the thesis of noumena seems at first sight credible, is that we have experience of different sense-modalities, each implying that the others are incomplete, and we have memory of changes in our experience and/or its interpretation over time, so that our conceptual knowledge (or its suppositions) has naturally come to conclusions that ‘things are not quite or always what they seem’. But in such case, the term noumenon is trivially but another name for abstracts or concepts. In Kant’s coinage and use of the term, however, the noumenon is not a hidden extension of the phenomenon, but purports to discard and replace the phenomenon altogether. The noumenon is by definition unknowable (universally) – though Kantians never tell us how come they themselves have the privilege to even know enough about it to know that it exists and is unknowable! The correct statement would rather be that noumena (i.e. less abstrusely, abstracts, concepts) are not concrete experiences, but merely logically assumed derivatives of percepts. They are hoped to be ontologically ‘more real’ than percepts, digging deeper into reality than the visible surface of things (to which we are supposedly restricted somewhat by the limited range of sense-modalities open to cognition), even as they are epistemologically admitted to be less reliable.
The laws of non-contradiction and of the excluded middle are intertwined with that of identity, as evident in the arguments above. But how do we know that ‘A is not non-A’ or that it is either-or between them? Consider our basic dot of light or its absence (darkness) in the visual field – such a dot is evidently never in contradiction with itself. We never simultaneously perceive a dot and not-perceive it – in any given place we mentally chose to focus on, there either appears or does not appear a lighted (or dark) dot. At this level, where the object is reduced to a single character (light) and precise place (the smallest possible size), we cannot honestly, sincerely answer ‘yes and no’ or ‘neither yes nor no’ to the question. It is there or it is not. If it seems there, it is. If it does not seem there, it is not. We cannot even pretend we don’t see what we see – at least not in words, for we would have to acknowledge their meanings, and therefore the actual phenomenon.
These laws are indeed in the phenomenal world, insofar as positively no phenomena ever appear in contradiction or as neither-nor, i.e. by absence of empirical evidence to the contrary. They are in, because their negations are not in. But they relate to mind, inasmuch as when a dot A appears and we start speaking of the unseen non-A, we are in fact imagining non-A in our heads, and so bring a new (mental) element into the picture. By the law of identity, this non-A phenomenon (which is mental) must be distinguished from its alleged opposite A (the given, which may or may not be mental), and admitted as an addition in the experiential field. But it remains true that A and non-A themselves are not in fact coexisting or both absent in the field – rather what we experience is coexistence of the given A with a projected non-A.
The law of contradiction does not deny the possibility that two different things might coexist, like a dot of light and the imagination (or memory) of absence of such dot of light; such things are merely contrary. The law of the excluded middle does not deny the possibility for something and the idea of its absence to be both absent from a field of experience; in such case, we can still suppose, as we indeed see as experience, that the thing itself is absent (even though the idea of its absence is allegedly absent – until mentioned as absent, that is!). Thus, these laws are empirical, in the sense that they do not impose anything on the phenomenon, but accept it as is. They merely push the observer back into the fold of experience, should he venture to stray. They do not involve a modification or manipulation of the phenomenon, but on the contrary make the observer openly and carefully attentive to what is phenomenal. They involve a distinction between primary phenomena (be they ‘material’ or ‘mental’), as given ab initio, and imaginary alleged representations (ideas, mental phenomena) of eventual phenomena, which merely introduce additional phenomena.
It is very important to emphasize again that negation is a logical act. It is never a pure experience, but always involves conceptual interference by the Subject. In formal logic, terms like A and non-A are neutral and formally indistinguishable. That is, they function in interchangeable ways, so that the negation of non-A (non-non-A) is technically equivalent to A (by obversion); and we might label non-A as ‘B’ and A as ‘non-B’ without affecting inferential processes. But at the phenomenological level, these labels are quite distinct. Something appearing would be labeled positively (say, A), whereas something not-appearing would be labeled negatively (as non-A).
What we here labeled A is a phenomenon or percept. What we here labeled non-A is not apparent per se, but only effectively ‘apparent’ in that A did not appear. Non-A signifies that we have asked a question ‘is A there (i.e. in the phenomenal field)?’ and after further scrutiny answered it by ‘no, I do not find it there’. The former (presence) is directly known, the latter (absence) is indirectly known through a mental projection (imagining A, i.e. inventing it or remembering it from previous perceptions) coupled with an experimental search (whose result is unsuccessful). Clearly these are very different cognitions – one being purely passive and empirical, the other involving an active inquiry and referring to observation only by the failure to confirm an anticipated equivalent of one’s imagination. The later is useful and informative, but it is a construct.
Negative concepts or statements are thus never strictly-speaking empirical, and negation is a fundamental building block of reason. A negation is at the outset, by its very definition when introduced by the Subject as a cognitive artifice, logically contradictory to something. It cannot then be said empirically that both percepts A and non-A occur (since saying I ‘see’ non-A in the present field of perception just means I looked for and did not see A in it), nor that neither A nor non-A occur (since if I look and do not see A in the present field of perception, I would conclude non-A for it – though I may remain open-minded about other eventual fields of perception containing A). A negative concept or statement is therefore fundamentally different from a positive one, and can at best only indirectly ever be characterized as ‘empirical’.
The three laws of thought are logical primaries, involved in all discourse about any phenomenon (and similarly relative to intuitive data, and at a later stage with respect to conceptual discourse itself). They jointly operate in identical ways in every observation, pushing us to admit what we see (identity), not to contradict what we see (non-contradiction), and not to ignore and add possibilities to what we see (exclusion of a middle). To fail to apply them is simply to confuse the given data with additional mental ingredients (fantasies), which neurotically either deny the evidence (mentally replacing it with its contradiction) or question it (by mentally proposing a ‘middle’ term). These laws can be stated as propositions, but they nevertheless have no conceivable alternatives. Any doctrine proposed has to be reconciled with experience somehow, since all discourse is a reaction to experience, an attempt to solve the mystery it presents, so merely ignoring experience does not qualify as reconciliation.
In that sense, it is accurate to say that these laws are laws of thought; they are laws for the mind (the observer). We may say that something is A and not A, or neither A nor not-A. But these words have no meaning in experience, no phenomenal referents. They are just words, sounds or drawings that signify nothing, not even an imaginable circumstance. The way we ‘imagine’ them is to stupidly or deliberately confuse a thing and an image of a thing, and project the idea of non-A (instead of non-A itself) next to A (or next to the idea of A) or some such artifice. In other words, the propositions claiming to deny the laws of thought have only a superficial meaningfulness and credibility, due to in fact having referents (ideas) other than those they pretend to have (things). With regard to the original objects of perception, they are in fact silent.
Note well that application or obedience the laws of thought does not involve an imaginative act (a volition); it is on the contrary attempts to ignore or deny them which do, requiring interference of the observer’s imagination in the cognitive process (preempting experience). That is, the laws of thought themselves are objective, it is only their denials that are subjective (in the pejorative sense). The laws of thought thus remain empirically, and epistemically, and therefore epistemologically, undeniable. So much with regard to applications of the laws of thought to perceptual evidence.
With regard to concepts (which derive from comparisons and contrasts, or from subsequent imaginations recombining such concepts) and propositions (imaginations of relations between concepts), they remain always open to doubt, hypothetical, so long as equally credible alternatives are imaginable. Credibility is found in everything experienced or thought, it is merely admittance that such and such has been experienced or thought (thought being a sort of experience, though mental). Ab initio, any two concepts or propositions are compatible, having both been thought. Incompatibility is a later judgment, which follows realization that the concept or proposition somehow directly or indirectly contradicts experiential evidence or leads to internal inconsistency in knowledge or is inherently self-contradictory.
If two such ideas or thoughts are found or not found to be in utter conflict, they both retain the minimal credibility of being at least imaginable, at least till one or both of them is found incoherent with some experience(s) or for some reason unimaginable. If for some reason they are considered to be in conflict, they separately retain some credibility, though their interaction raises a doubt and it is understood that we have to ultimately eliminate at least one of them, removing its temporary credibility with reference to further experiences or abstract considerations. During the phase of doubt, we may refer to their frequencies of confirmation in experience, and regard one as more credible (or likely or probable) than the other.
Words are sounds, sights or touch symbols that conventionally refer to phenomena, intuitions and abstracts. As sounds, sights, etc. per se, words are of course themselves phenomena, which can be expressed either materially or mentally as outer or inner speech or writing, being used for personal thought and memory or social communication and knowledge accumulation. Many words have rich natural and historical roots, but they are nonetheless conventional (i.e. arbitrarily chosen), in that they can always be changed at will by consent. Also note, the equations between word-sounds and word-sights (and likewise, felt-words) are also conventional.
Words evidently differ from language to language, from one population group to another. A language is a collection of words (vocabulary) used by someone or some group, in accordance with certain accepted rules (grammar). Words, for old or new things, are almost daily coined and adopted by individuals, social groups and societies. Whoever coins a word, for whatever purpose, must intend (chose, convene) some more or less stable signification for it. Without such an intuitive understanding, words cannot have any semantic content.
Words are not mere phenomena, but refer to things; i.e. these auditory, visual or touch phenomena are signs for things (phenomena, intuitions and abstracts) other than themselves. Whether the things they refer to are real or illusory, clear or vague, is not logically relevant to the fact of signification. Signification is a relation, one of equation of sorts, saying (i.e. intending, to repeat) ‘when I mention this word, please think of this thing.’ Words are labels, they have meaning. There are wordless thoughts; indeed most of thought is wordless. In the case of wordless thought, one is conscious of the meaning without use of the label.
Indeed, it is ultimately impossible to understand, use or discuss words without appealing to wordless thoughts. If (as some philosophers claim) words obtained their meanings only by equations to other words, there would be need for an infinity of words; and since that is not possible (language is limited in size, and anyway man has no time for infinite regression), the most basic of words, from which all others derive, would be meaningless; and thus all words would be meaningless. But to claim (in words) that ‘words are all meaningless’ or that ‘words refer only to other words’ is self-contradictory, since such claim itself purports to have understandable and communicable meaning. Such claim is thus not a consistent thesis, and can be rejected once and for all. Therefore, it is logically self-evident that some words are meaningful, and that as well as words with explicit meanings, there are wordless implicit meanings.
The meanings of words, as we said, may be phenomenal objects (e.g. ‘Avi’ refers to an individual physical person, but also ‘person’ refers to all persons), intuitive objects (e.g. ‘I’ or ‘I want’) or abstract objects (e.g. ‘personhood’ or ‘wanting’). But moreover, more importantly, every word implies an intuition – the intention that the word concerned be associated with such and such a meaning being itself an intuitive object. We intend the meaning of a word, not only the first time, when we coin it or learn it, but every time thereafter, whenever we use it. Without such intention, the word remains a mere noise or shape, devoid of meaning for us. Words in themselves are inert; it is our intentions that give them life and power.
Each of us knows (in the way of self-knowledge, intuition) what he means by the words he uses at a given time, whether clearly or vaguely (and whether correctly or erroneously according to previously accepted conventions). This is evident in the fact that when we think or communicate, we do not and do not need to explicitly list out all the words in our language and map all their proposed interrelations; thus, our discourse at any given time is mostly wordless and the words we do use at the time concerned must be admitted to be ultimately wordlessly intended to refer to certain things, whatever they be.
It is therefore incontrovertible that we have self-knowledge of our intentions, with regard to words at least – i.e. the fact of intuition is unavoidably implied at least by the fact of language. This is an interesting and important rational proof of the existence and knowability of at least some intuitive objects (objects of self-knowledge), incidentally. We can confidently say that intuitive objects exist, as any attempted discourse to deny them meaningfully itself logically implies intentions (as to the meanings of the words used) and therefore (some) intuitive objects. Thus, the postulate that there are intuitive objects is not an arbitrary claim, but a hypothesis for which we have found empirical (concrete) confirmation in the fact of language and its rational (abstract) implications.
Putting our ideas (terms, propositions, arguments) into words is called verbalization. Regarding the meaningfulness of words, what misleads many skeptical philosophers is the observation that words often have uncertain, vague and variable meanings. Starting from the assumption that words have to have real, precise and unchanging meanings to be at all meaningful, they conclude that words are otherwise meaningless. But this is a mistaken view, based on the misapprehension of word-meaning as equivalent to definition (by means of other words, as above described) and on a model of knowledge as a closed-circuit and static body of (verbal) information.
In truth, as careful observation of our actual behavior reveals, knowledge acquisition is gradual and adaptive. Our experience is cumulative and our rational reaction to it is a developing and evolving thing. There is no single item or total body of knowledge that stands alone and final; and the interrelationships between items, including the rules of interrelation, are always subject to review and revision. Knowledge is inevitably contextual, implying an unending trial and error process. It is not (verbal) definition that gives meaning to words; definition is only an attempt to put into words and delineate what we already wordlessly intend. A definition is like any other proposition subject to empirical, intuitive and rational checks and balances. It is an inductive product, not a deductive preliminary.
When we come across a new appearance (be it phenomenal, intuitive or abstract), we may find fit to label ‘it’ for purposes of memory and further discourse. What we mean by ‘it’ (a physically, mentally, intuitively or verbally indicated, i.e. pointed-to, object, a ‘this’) is always tentative and open-ended. As we proceed further, thanks to new experiences and reasoning, this intended meaning may become firmer or shift or even entirely dissolve. First, ‘it’ may seem clearly understood; then we come across new phenomena or have new thoughts which make us realize that the initial intention is uncertain or unclear and we have to adjust our focus, and make further differentiations so as to pin-point more precisely what we ‘really’ intended by it; and so on, successively. Sometimes the intention remains unchanged, but our initial verbal definition (if any) may turn out to be inaccurate (too broad or narrow or otherwise inappropriate) and require modification. In some cases, we come to the conclusion that there was no need for a new word, and either abandon it or accept it as a mere synonym. In some cases, we realize that the term was already assigned to some other object, and keep it mind that it is a homonym.
Words are primarily intended to express (assumed) facts, but they may also be used – inadvertently as well as consciously – to signify fictions. We are quite able to distinguish a sensory phenomenon from an imaginary one without demonstrated sensory equivalent, and register the names for each with appropriate caveats. The intended object of a word may at first be thought real (as all appearances tend to be), and then after further information and reflection (which sometimes stretches over centuries), be found illusory. In such cases, the word may be dropped altogether – or kept for historical or literary purposes with the understanding that what it refers to is fictional (e.g. ‘unicorn’). These observations in no way justify a general condemnation of verbalization, but are events we take in stride without difficulty.
‘Universals’ (a venerable philosophical term) is another word for abstracts, referring firstly to the presumed something underlying identifications of distinct sameness (e.g. the squareness of two square objects), and at a later stage to whatever may lie behind more complex products of conception (involving imagination as well as logic); that is, all the end-results of interpretation, of reasoning about the perceived outer and inner world. Furthermore, we assume that there are also objects of intuition (i.e. self-knowledge), and these may also be compared and reasoned-about, and give rise to concepts.
We can safely assume that, in some cases at least, universals/abstracts/concepts have an ontological significance, and are not merely mental constructs referring to nothing beyond themselves. For to deny all concepts such reality, is to deny truth and meaning to one’s own assertion too, since that skeptical assertion itself is wholly composed of concepts. It follows that at least some concepts must be admitted as having a presence independent of any thought about them. (Precisely which concepts are to be admitted is what the science of Logic is all about.)
As to the nature of universals, my own theory (derived largely from modern physics and Buddhist ideas) would be that universals are, effectively, mathematical formulas. If I compare two waves, all the measurements I perform in doing so can be expressed by means of the algebra of coordinate geometry. Such formulas, or rather the relative measures of the waves’ features, motions and relations signified/implied by the formulas, are what we call ‘universals.’
If the waves making up two particulars are wholly or partly equal or proportional, in respect of their varying shapes and sizes (length, amplitude), positions, trajectories (directions), speed, frequencies of conjunction or non-conjunction with others, then the particulars seem are ‘similar’ to us, and their common measures can be used to define concepts. Thus, universals (portions of waves, or of their histories) can be found in two or more particulars (full waves); and further abstracts can in turn be based on such abstracts (in the way of portions of portions of waves).
The magnitudes or degrees of the features, movements and interactions of waves (universals) are not the waves themselves (particulars), yet the waves cannot exist without having measures. We perceive the waves and we conceive the formulas, but both are in a sense equally there, apparent in the phenomenal object of experience. For this reason, even abstracts are sometimes regarded as quasi– or virtually experienced (thus broadening the term ‘experience’ to cover all appearances).
The waves and their measures cannot be dissociated within the field of experience, being respectively entities and attributes or behaviors of entities. What reason does to ‘draw out’ (abstract) the measures, is to focus on them while mentally ignoring the waves (or any images of or symbols for the waves). One cannot normally directly know the measure of a single object; one can only do so by considering and comparing a plurality of (two or more) objects. Even when the intuited self conceives of ‘a self,’ although it has no direct experience of other selves, it refers to the many times it has intuited itself.
Thus, a universal can be said to transcend experience, yet be somewhat in it or immanent – it straddles experience. A universal is not in some metaphysical Platonic repository of Ideas, nor merely in the mind of its beholders (though it may also be there, when some external wave induces a like internal wave in a mind); it is inherent in every complex of wave-forms with the selected common mathematical characteristics.
This explanation is not intended as a mere metaphor– it need not be limited to imagined waves, but can be extended to all concrete existents. If light and gravity are waves, elementary particles are complicated bundles of such waves, sound is a wave (movements of air masses), and if the other sense-modalities are ultimately wave-like (as the electrochemical events associated to sensation suggest), then all material and mental phenomena, including living beings, may be said to be waves.
These waves all occur and travel and interact within a space and time as voluminous as the universe, conceivably as moving deformations of some primordial fabric (the stuff of ‘existence’). They vary in complexity, ranging from brief and short events (unit waves, say) to the 3-D pulsations of quarks, photons, neutrinos, electrons or atoms, molecules, and to larger and larger collective wave motions of the later. Not just sights and sounds, but all sense-modalities, material or mental, including whole living organisms, are in this view varieties of wave or wave-motion formations.
And perhaps not only objective phenomena, but also subjective (i.e. intuited in/by the Subject) things and events might be supposed to have this fundamental wave character.
Wherever waves (particulars) appear, their measures (abstracts) are inherent in them. So we can say that, although universals are not normally additional extensions in the experiential field (i.e. not themselves discernible wave events), they are still somehow present in it. They are normally only known through interpretative efforts (comparing and contrasting two or more waves). This theory of universals as mere measures of things assumes all things are reducible to wave activity (in some primordial substratum, perhaps – yet not an ether, somehow).
In that case, the complex waves we call the sensations can well be construed as wave signals transmitted from one end of the sense organs via the spine and/or brain over to their other end where the observer observes them. Similarly, memories may be supposed to be wave signals stored and sustained within the brain for occasional recall. That is, the senses transmit energy or fields onward to the Subject, from the ‘outer’ region of his experience, comprising his apparent body and its material surrounds. Memory may thereafter be produced, reverberating with the same vibration.
With this thesis, we are not forced to assume that the waves are distorted in transmission or storage, since our premise is that the terminal wave is a continuation of the initial wave. In such case, the message received (by the observer) does not just resemble the original message (captured by the sense organ’s receptors or stored in memory); it is the original message, which has vibrated through the senses, and possibly memory, to us without refraction. Assuming uniformity, the beginning and end waves are just the same object at a different time – a single traveling (wave) object. They may be of different substance (material, in whatever way, or even a mental product of material waves) and even magnitude (though with due proportions), but their form must remain the same. The universal is that form – the mathematical characteristics (including motions and interactions, as well as features) of the wave.
Thus, when I see or remember a bird, say, I can rightly consider that I am in direct contact with the bird; I am experiencing the waves emitted by the bird that reach over (via the senses, or memory) all the way to me the observer. The waves are the bird, the part of it that flows over into my body. This is not a mystical statement, but one quite physical. Any delimitation of the bird (or any object) in space and time elsewhere than at the very limits of its range of physical effects is arbitrary.
In this view, then, the sense organs (themselves wave complexes, like all matter) are filters for particular classes of waves (fine light waves, gross sound waves, atomic wave bundles, electrochemical bundles of waves, whatever). Each sense organ is capable of receiving and passing on only specific wave-forms, leaving out all others; each specializes in a sense-modality (or group of sense-modalities), insensitive to others. The eyes exclude sound waves, the ears ignore light-waves, etc. These waves would be the same in form if they had been encountered immediately and not vibrated though the senses; the senses only isolate them from their context. Therefore, we may indeed not see all the waves out there, but those we do see we generally accept as equivalent, as mere continuations of the original disturbance in space and time.
Similar comments can be made with regard to memory, note well. Once the sense-object has been perceived by the Subject, after relaying the waves concerned by sensory processes, the wave is stored (electrochemically, as neuroscientists teach us) in the brain. That is, we can well suppose, the wave itself is artificially made to continue existing in the way of some activity in the brain. Thus, in this view, the neurological ‘imprint’ is not a mere coded symbol of the original message, it is the original mathematical message. In such case, even while admitting that the message may occasionally be dampened, hard to recall or even lost, there is no need to figure out how come it (usually) stays the same. When we evoke a memory, or recognize a repetition of a sense-object previously encountered, we merely use the ongoing physical wave deep in the brain to produce a perceptible mental wave, identical in form to the stored one and to its sensory origin, projecting it (as an more or less vivid image) apparently inside our mind (for reminiscence) or outside it (for comparison to the new sense-object).
What is true of memory of sensations is equally applicable to memory of abstracts based on such sensations, since as above postulated such abstracts are merely mathematical aspects of the wave-forms of the original sensations. Thus, we can understand without difficulty how abstracts are concretely stored in memory. As for mental projections (imaginations, perhaps feelings) and objects of intuition, and abstracts derived from them, supposedly they have allied physical vibrations in the brain (i.e. each of those thoughts has a specific physical effect, which therefore ‘corresponds’ to it), which may be stored in memory and recalled.
Some philosophers would object that the waves sensed or remembered may well, for all we know, change form as they tumble through the sense-channels, or within their memory storage. But in such case, we still have to appeal to the senses and memory to invalidate particular sensory or memory experiences – otherwise, how do we claim to know that error occurred? So we can only logically suppose occasional distortion.
They could instead argue that the waves we experience are not as they seem end products of sensory processes, but independent events merely contiguous with them. But in such case, the impressions that we have a body, with a brain, spine and sense organs boiling with activity, would remain unexplained phenomena, leaving a gap or loose end in our understanding of the world experienced. To integrate all phenomena into our world-view, we need to include consideration of the phenomena we call the sense organs, etc., and suggest why they are there, what their role might be in the wider context of experience.
Thus, extreme skepticism is self-defeating, whether by inconsistency or by incompleteness. At first sight, the sensory and memory processes might be supposed refractive, producing an image very different from its origin. We however cannot logically claim that this is definitely true, because such statement would require cognition of sense-objects without reliance on the senses, or of memory-objects without reliance on memory. The critic would be claiming special cognitive privileges not granted to the rest of us.
Our present account approaches the issues from another angle – phenomenologically. Start with the phenomenon as a whole as given; the only issue at stake is then: what is the possible relation between these two aspects of it (the objects classed as external and those classed as mental-images produced by the senses or the brain)? In that case, we may assume that the senses and memory relay the information and do so without affecting it, with much less pretensions. For we only claim to relate together two factors (the material object allegedly sensed or remembered, and the subsequent sensory or memory processes presenting a mental image at the interface with the observer) which are already in the field of consciousness and accepted as existing (whereas the opposite view lays claim to things outside its own awareness by its own admission).
We are only attempting to explain the existing situation, that a process takes place through the senses during perception of physical matter or in the brain during its recognition – what is the role of these evident processes, we ask? If we assume there is always refraction, we are making a statement denying our experience of the matter at hand. But we may well, i.e. consistently, assume that not all sense or memory information is faithfully transmitted, so long as we can determine the matter by some other, more reliable sense-data (and, often, of memory-data). We thus prove that (some) sense and memory data is trustworthy.
We may wish to confirm sense evidence scientifically, by means of experiments showing that the information indeed stays the same from reception by the senses to presentation to the observer, in the way of a physically discernible persistent vibration, whatever its comparative size, depth or substance. Similarly, we could look for an ongoing physical vibration of some sort in the brain, before definitively concluding that memory is stocked as specific wave-forms. But the issue is really not empirical – it is logical (which means in practice that even if we don’t immediately find something, we have to keep looking).
Say we find no evidence of persistent wave-forms; we would alternatively look for fixed formulas that ‘translate’ the original wave in some regular manner, so that even if the final wave does not resemble it they can be correlated. Claiming codification of sense or memory data is not the same as claiming lawless refraction; for uniform refractive processes would simply require that we ‘correct’ our world-view by ‘translation’, whereas random refraction (such that no correspondences whatever can be established) would leave us in confusion. But in the last analysis, even assumption of a regular code is not a viable theory, because it too ultimately makes contradictory claims, that matter is perceived and yet – because of sense or brain interference – is not perceived correctly (which means, not perceived period).
So we must conclude, whatever experiment reveals, that ‘some sense and memory experience is valid’ is a logical truth. That is, no experiment being possible without this truth, none can belie it!
We do not need an epistemological ‘axiom’ to defend sensation and memory as universally reliable. It suffices to consider the products of these faculties as true until and unless found false. That is, the assumption of their essential correctness is an inductive principle, rather that a deductive credo. No artificial forcing of the issue is involved. Every event of sensation or memory is granted initial credibility, while remaining open to eventual sensations or memories that may put the preceding in doubt. When and if particular contradictions occur, they must be sorted out in accordance with normal logic.
It should be noted that the wave theory of universals proposed is the only coherent theory available. If we consider other proposals in the history of philosophy, we find them all to be logically flawed, and so in fact incapable of dealing adequately with the problem of universals. Thus, Plato’s Idealism, according to which the explanation of the common characters of different things experienced in our world are that they reflect certain transcendental “Ideas,” gives a wrong impression of solving the problem while in fact only sweeping it under the carpet. The Ideas existing in a higher world are only less numerous than the things in our lower world, but they are still a plurality with some common characters. In that case, what of their common characters, such as “transcendentalism,” “ideality,” or existence – are they in turn representatives of a single, unitary, top world? And how would this One Grand Idea break down into the Lesser Ideas?
A more immanent view of universals, which could be regarded as effectively the current “common-sense” view, would be that different primary substances are scattered throughout the universe and combine in different ways to produce the things we perceive through the senses. Alternative theories can be proposed as to what to regard as these material substances: they might be distinct sensa (i.e. units of sensed light, sound, etc.), or perhaps qualities (the minimum number required to construct things) rationally inferred from sense data. Some suggest instead that universals may be mental or verbal constructs – i.e. imaginations or subjective inventions or mere words in our heads. Whatever we construe them to be, the (material or mental) theories of universals as substances suffer from the same flaw as Plato’s theory: we are still left with the need to explain a plurality (albeit a smaller one), and derive it from a unity (existence).
The above ‘wave’ theory of universals, granting its premise that everything is ultimately reducible to ‘waves,’ i.e. mobile vibrations in some sort of continuum, leads to the very radical conclusion that ‘all things are one.’
The world as it appears to our touch-organs or to the naked eye – or even the eye aided by microscope or telescope – may give the impression that dimensionless points, lines or surfaces exist in nature, but as Physics has evolved it has become clearer that physical objects do not have precise corners, sides or facades – but fuzzy limits, arbitrarily defined by the visibility to our senses (specifically, sight and touch), aided or unaided, of concentrations of matter or energy.
For example, the tip of my penknife may seem like a sharp “point” to my touch or sight, but it is really – according to physical science (i.e. upon further investigation and reflection) – a rough, voluminous conglomerate of atoms, which are themselves complexes of smaller and smaller particles (electrons, protons and neutrons, seemingly some distance ‘apart’ from each other, etc.), which are themselves without beginning or end being really vague clusters of waves. Similarly with regard to the cutting edge or flat sides of my penknife.
Indeed, if one takes these considerations to their extreme conclusion, one could say that no object has a beginning or end, every object stretches to the ends of the universe or to infinity, and what we refer to as a specific individual object is merely the most humanly visible or concentrated part of that whole, which we arbitrarily or conventionally consider a separable unit (and habitually name, to solidify our viewpoint). So that ultimately, there are in fact no individual objects, but only ripples in the single object that is the universe as a whole.
Where does an atom (or any other body) begin or end, granting that all consists of waves? If we see a star billions of miles away, on what basis do we say that the star ends over there, while the “light from the star” is here? Rather, we ought to say that the light we see is part of the star, i.e. that it extends all the way to us (at and through our visual sense organs, and on to our memory) and beyond. At what distance from the star do the gases or the light it emits cease to ‘belong’ to it, and are to be considered as ‘separate’ bodies? The cut-off point can only be arbitrary, i.e. mere convention. Gravity operates at astronomical distances. What objective ground do we have for distinguishing a field from its apparent origin? Furthermore, stars are in constant flux, arising in time and disappearing in time. At what point in time (as well as space) may we claim that the matter and energy we now call a star is ‘not yet’ or ‘no longer’ a star? Surely, the quarks from which the star emerged were already ‘the star’ and when the star bursts or is absorbed into a black hole it is still ‘the star.’ We ourselves are stardust – does that mean that the stars in question became us, or that being a star – from the beginning of time to its end – includes eventual human forms?
In this view, every entity in the universe stretches out with every other to fill the whole space and time of the universe! And if we say this, we might as well say – without any mystical intent, though in agreement with Buddhist mystics – that all things are one. There are just more intense concentrations of matter or energy here and there, now and then, in one continuous field, but nowhere dividing lines. Because we perceive only fractions of the totality, only the aspects involving the sense-modalities, we isolate small blobs of the whole as individual phenomena. All phenomena perceived are centers of complex wave activities in the universal fabric; We ‘individuate’ phenomena with reference to the sense-modalities they exhibit which are accessible to our senses. We regard as delimiting an individual object in space and time such perceivable fraction (visible to the senses) of the wave activity stretching to the ends of the universe – ignoring its larger invisible extensions, later induced by reason. Thus, all individuation is fantasy (this can be known by rational considerations, as here), reinforced by naming (itself a sense-modality phenomenon, by the way). In which case, strictly speaking, nothing is divisible at all.
That would seem to be a correct view of our physical world in the context of present knowledge – the hypothesis most consistent with experience, experiment and current scientific theorizing. We thus, provided we anticipate the results of Physics and claim that some sort of unified field theory is sure to be established, and provided we stretch that assumption to include wave explanations of the mental and spiritual domains, arrive at a concept of the world as ‘unity in plurality’ – a harmonious marriage of the philosophies of Pluralism and Monism. Heraclitus was right – everything is ultimately motion (i.e. waves) and Parmenides was right too – everything is ultimately one thing (i.e. the medium subject to waves).
We could even view this conclusion as a justification of the Buddhist view that “all things are empty!” For instance, the message of The Diamond Sutra seems to be that all objects material or spiritual are infinite vortices with no beginning and no end. They are neither categorical as they seem; nor can they be surely declared hypothetical, being delimited merely by our naming of them, but having no sure limits in themselves so far as we know so that they are therefore effectively boundless.We have already, inspired by Buddhist doctrine, concurred with them that individuation is a man-made artifice. But even granting that we might legitimately, out of mere convenience, focus on specific places and durations of the universe, because a disturbance ‘stands-out’ there and then in relation to our senses – we are still left with the question as to what it is that is disturbed? What is the medium or substratum of all wave motions? We are tempted to view it as a stuff and call it “existence,” or like Descartes call it “the ether.” The problem is that since the Michelson-Morley experiment on the velocity of light such a substance underlying waves has apparently been discredited. These physicists measured the velocity of light in the same direction as our planet’s motion and in the opposite direction. To everyone’s surprise, they found the velocity identical either way. This was eventually explained by Albert Einstein as indicative that there is no absolutely stationary substratum or “ether” relative to which wave motions occur, and he built his famous theory of Relativity as an alternative world-view (such that space and time coordinates are depend on the velocity of the observer relative to what he measures).
Thus, although when we think of waves,
and mathematically work out their motions and interactions, we regard them as
disturbances within some medium, it turns out that there is no such medium
according to experimental indices! On this basis, we can agree with Buddhist
philosophers that (surprisingly, incomprehensibly) nothing is being waved
– i.e. that the ultimate nature of “existence” is “emptiness.” And
there is no need of high meditation or mystical insight to arrive at this
conclusion – it is seemingly justified by ordinary experience and reason
(scientific experiment and theory).
 In such case the mental projection does not entirely blank out an identical material object, but effectively hides it sufficiently.
 The smaller one will be placed relatively closer to the observer than the larger one, and both may be gradually rotated, so that all their ‘sides’ are effectively juxtaposed and compared. Such manipulations are regarded as mere positioning of the objects, and granting the hypotheses underlying perspective including continuity of adjacent phenomena the objects themselves are not affected thereby.
 In chapter 5.
 It should be kept in mind, in this context, that color, sound, odors, tastes, touch-sensations and feelings all seem to have spatial as well as temporal aspects, which give rise to our correlations of sense-modalities. Thus, the sense of depth in the surrounding material world is not only due to perceptions and conceptions of perspective, but also to various sound and touch sensations, which add body to visual depth. The sounds or smells we experience have direction, with reference to movements of their external source in space or of our body relative to it. The food we eat has a location and shape/size and texture in our mouths and tongues, a hardness or softness and certain sounds under our teeth, not just a taste and smell. Such inferences of spatiality are based on very complex hypotheses involving both perceptual events and conceptually assumed causes and conditions.
 For instance, I can recognize a smell as that of a rose, i.e. as similar to smells previously experienced and classified as rose, even though I don’t seem to be able to reproduce an ‘image’ of that smell in my head at will. But interestingly, in a dream I might apparently ‘smell’ a rose, though none is nearby. No doubt also, different people have different facilities in respect of perceptualization. I am sure some people can visualize things in their heads better than me, so maybe some can actually imagine the smell of a rose.
 Indifference is sometimes counted as a third kind of sentiment, though strictly referring to lack of sentiment. That is of course because the absence of pleasure or pain signifies underlying value-judgments that exclude interest by the Subject in the object concerned. Additionally, we should note that some sentiments are of uncertain polarity, i.e. we find it difficult to say whether they are pleasure, pain or perhaps both at once. This is said apart from the fact that one thing may cause opposite sentiments, as e.g. when a masochist is whipped and feels both pain in his back and sexual pleasure. I here mean that one and the same sentiment may be ambiguous (so that the Law of Non-contradiction may not be applicable with reference to pleasure and pain, i.e. they are not strict contraries). Similarly, and all the more so, with regard to abstract feelings.
 How precisely that occurs with regard to the other sense-modalities is admittedly left vague. We should regard comparisons and contrasts in these sense-modalities to be less reliable. Ultimately, I think, we have to refer to a theory that these other sense-modalities consist of vibrations subliminally perceptible to some degree by being somehow reducible to light phenomena, comparable with reference to correspondence of dots. Similarly with regard to intuitions.
 See Future Logic, chapters 2 and 20.
 See Future Logic, chapter 31.
 Our minds seem so made that, indeed, we might consider that we always think non-A when we see A. This is not a mere perversion of the mind, it is rather an expression of the fact that concept-formation involves not only reference to perceived similarities between two objects, but also to perceived dissimilarities between other objects and them. Thus, in order to classify something as A, we must simultaneously declassify it from non-A. That is, the thought of A automatically calls forth the thought of non-A, for purposes of distinction. It is not that A per se implies non-A (though in most cases, A in one thing implies non-A in others, otherwise neither A nor non-A would be distinguishable in the first place), rather it is that A cannot be fully delimited or understood without bringing to mind non-A as a possible alternative (except perhaps ‘non-existence’ – though in that ultimate case, we can say that the term is merely verbal, without conceivable concrete referent). Furthermore, concepts formed by negation (like darkness) presuppose some relatively positive phenomena (like light), whose absence they express, having been conceived first.
 Of course, at a conceptual level, i.e. when dealing with abstracts, we may encounter contradictions (i.e. both A and non-A seeming true) and doubts (i.e. neither A nor non-A seeming true). Here, both the positive and negative concepts are mental constructs, and so there is no guarantee that the issue can immediately be resolved by one look. That is of course where the whole science of logic comes into play; it is needed to deal with just such issues with reference to a plurality of experiences.
 We consider concepts or propositions compatible until and unless we find some incompatibility between them. As I already pointed out in Future Logic, in opposition to the claims of certain modern logicians, we do not ‘prove consistency’ but rather ‘find inconsistencies’.
 For instance, blind people use touchable words (Braille); certain pre-Columbian peoples used knots in rope as words.
 Thus, e.g. the sound of ‘Avi’ and the written letters A-v-i have no relation other than what we have convened for them, though that convention has a rich history that we will not needlessly ignore.
 Similarly, the claim that words are mere conventions implies that ‘knowledge is conventional’ is confused. First because that proposition, as a factual assertion, claims to know something beyond convention about knowledge; whereas applied to itself, it denies the possibility of non-conventional knowledge. But furthermore, all conventions imply factual knowledge: you have to know that there is a convention and what that convention is supposed to be and how to apply it correctly! You cannot have a convention about a convention… ad infinitum – it has to stop somewhere factual.
 Comparison involves two objects, as already stated. This does not mean that comparison is impossible with only one extended object under scrutiny, for we may be able to compare parts of that object together. We may, for instance, compare the sides and corners of a single square: the resulting concept is not the square figure as such, but concerns more specifically lines and angles. Even then, the concept is incomplete till we contrast other lines and angles.
 I here count identification of sameness and difference in concretes, and of their conformity with the ‘laws of thought’, as among acts of reason (the first and simplest of them) in that they result in conceptual information. They are however so basic and relatively brief and devoid of process (direct) that they seem akin to perceptions. We could also, and often do, regard them as a distinct class of objects – objects of conceptual insight, as against ‘conceptualization’.
 I have note well excluded from this class, of objects of intuition, claims to direct knowledge of objects beyond oneself, e.g. claims to sensing ghosts or reading other people’s thoughts. These claims must be regarded, ab initio at least, as pretentious. While it might eventually be demonstrated by experiment that some people do have such extrasensory cognitive powers in some circumstances (e.g. by finding what they predict as thought by others as reported always or usually true by the latter, although no physical means of communication between the two were possible), the need for careful demonstration remains in every case an epistemological necessity. We cannot naïvely accept such claims as valid without resulting chaos in knowledge; they must be viewed as hypotheses to be confirmed by adductive means. Most people who claim direct knowledge of spiritual, intuitive, mental or material events outside themselves are simply not aware of the inductive processes involved in thinking, and tend to take their first impressions for granted without verification procedures.
 Here we of course have to go into detail regarding wave forms and mechanics.
 I do not mean to say that every time we think a universal we construct a precise mathematical formula. Ordinarily, people rarely if ever revert to advanced mathematics! I merely imply that we tend to such a formula, in a vague and approximate way – i.e. that if the mass of mental measurements and comparisons in our minds were correctly summarized, they would amount to a certain formula. Ex post facto extrapolation from fragmentary observations and notes is thus involved, in speaking of a formula.
 Looking at a large body of water such as a lake, you can get a visual image or analogy of what a universe of waves would be. You see bubbles, ripples and waves in constant flux, appearing, moving around, disappearing; these seem individual, in that the sunlight allows us to mentally draw boundaries for them, but they are all just the movements of one big entity; stir one place in the lake, and the motion is carried over to many or eventually (in diminishing degrees) all others.
 In view of the Michelson-Morley experiment and its sequel, the Relativity theory (see further on).
 Which was labeled ‘common sense’ by Aristotle, as I recall. Meaning, central sense.
 A bird, of course, is a complex entity, involving not only light waves from its plumage, but other sense data, like its physiology, its movements and behavior patterns, its call, its smell, even its taste. It is through consideration of all information about a given bird, in the same and other sense-modalities, and its comparison to other birds and things, that we decide whether, say, a visual message (apparent bird-form) falls in the category of ‘real’ bird, or is merely a photograph or statue of a bird. Errors do occur, not because the visual message is ever wrong, but due to not taking into consideration all information currently available (or later available).
 Although I say wave-form, I do not mean that sense-perception is perception of ‘universals’. The wave the observer sees (via the sense organ concerned) is still concrete; it is not merely the measurement of the original wave (a ‘universal’ or formula or abstract) that is passed on, but the wave itself or a continuing echo of it (a concrete manifestation). I only mean to remind that the wave has a form, indeed a constant one.
 This idea suggests that memory too is specific to the different sense-modalities; but it might also involve many sense modalities at once. As imagination is based on memory, it would be economical to store memories of complex sensory events in the various sense-modalities, so that they can be accessed separately in new combinations.
 I cannot at this stage say just why filtering is necessary, however. A plausible explanation would be that a direct universal consciousness would be overwhelming somehow, driving the observer crazy by the multiplicity of messages. For evidently, digesting data takes time, we have to ponder the interrelationships between the items of our experience, and indeed think about the validity of our thinking processes. We all know from bitter experience that if too much information and thought is required at any moment, we become confused. The sense-filters therefore probably help us to sort and order incoming data for analysis and synthesis. Yet immediate universal consciousness is precisely what Enlightenment-seekers work for and claim possible. According to them, reliance on sense-perceptions is an aberration to be avoided, sense-data being but a veil over reality!
 Such filtering may be considered not to occur in self-knowledge – there being no distance to travel between the observer and himself, or disturbances within himself (viewing here attitudes and volitions as waves or wave motions, perhaps within some distinct, ‘spiritual’ substance of the observer’s soul), no senses are needed and the observer knows himself most directly.
 The best metaphor for memory, in my view, is that of an echo chamber. I imagine a sight or sound (or whatever) channeled into a brain cell and there allowed to rotate on and on (storage function), until we decide to peek into the cell and see or hear the vibration once more (recall function).
 Note in passing that this skeptical thesis at least implicitly admits that internal objects (images) are correctly perceived by the Subject (within his mind), even if it claims them to be incorrect renditions of external objects by the sensory and brain organs. It has to do so, to have anything to discuss at all! Cognition as such is not in question, but only the assumed equation between different classes of objects.