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The Laws of Thought

A Thematic Compilation by Avi Sion

9. Compatibility or Incompatibility


1.     Apprehension


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[1], 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[2], 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).


2.     Explications


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!)[3]. 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.


3.     Negation


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)[4]. A negative concept or statement is therefore fundamentally different from a positive one, and can at best only indirectly ever be characterized as ‘empirical’.


4.     Primaries


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.[5]

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.

The job of Logic is, note well, not to exclude as much as possible, but to find ways to include as much as possible, so that all opinions and points of view (which all have some basis and so represent some kind of experience) are accounted for and explained or explained away. Logic is thus not merely, as some contend, search for contradictions, but (this in order to) search for harmonizations.


Drawn from Phenomenology (2003), Chapter4 (section 2).



[1]          See Future Logic, chapters 2 and 20.

[2]          See Future Logic, chapter 31.

[3]          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.

[4]          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.

[5]          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’.

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