Logic is founded on certain ‘laws of thought’, which were first formulated by Aristotle, an ancient Greek philosopher. We shall describe them separately here, and later consider their collective significance.
3.The Law of the Excluded Middle.
The Law of Identity is an imperative that we consider all evidence at its face value, to begin with. Aristotle expressed this first law of thought by saying ‘A is A’, meaning ‘whatever is, is whatever it is’.
There are three ways we look upon phenomena, the things which appear before us, however they happen to do so: at their face value, and as real or illusory.
We can be sure of every appearance, that it is, and is what it is. (i)Somethinghas presented itself to us, whether we thereafter judge it real or illusory, and (ii) this something displaysa certain configuration, whether we thereafter describe and interpret it rightly or wrongly. The present is present, the absent is absent.
Every appearance as such is objectively given and has a certain content or specificity. We can and should and commonly do initially regard it with a simple attitude of receptiveness and attention to detail. Every appearance is in itself neutral; the qualification of an appearance (thus broadly defined) as a ‘reality’ or an ‘illusion’, is a subsequent issue.
That statement is only an admission that any phenomenon minimally exists and has given characteristics,without making claims about the source and significanceof this existence or these characteristics. The moment we manage tobut thinkof something, it is already at least ‘apparent’. No assumption need be made at this stage about the nature of being and knowledge in general, nor any detailed categorizations, descriptions or explanations of them.
Regarded in this way, at their face value,allphenomena are evident data, to be at least taken into consideration. The world of appearances thus offers ussomething to work with, some reliable datawith which we can build the edifice of knowledge, a starting point of sorts. We need make no distinctions such as those between the physical/material and the mental, or sense-data and hallucinations, or concrete percepts and abstract concepts; these are later developments.
The law of identity is thus merely an acknowledgement of the world of appearances, without prejudice as to its ultimate value. It defines ‘the world’so broadly, that there is no way to counter it with any other ‘world’. When we lay claim to another ‘world’, wemerely expandthis one. All we can ever do is subdivide the world of appearances into two domains, one of ‘reality’ and one of ‘illusion’; but these domainscan never abolisheach other’s existence and content.
What needs to be grasped here is that every judgment implies the acceptance, at some stage, of some sort of appearance as real. There is no escape from that; to claim that nothing is real, is to claim that the appearance that ‘everything is illusory’ is real. We are first of all observers, and only thereafter can we be judges.
Reality and illusion are simply terms more loaded with meaning than appearance or phenomenon — they imply an evaluation to have taken place. This value-judgement is a final characterization of the object, requiring a more complex process, a reflection. It implies we went beyond the immediately apparent. It implies a broader perspective, more empirical research, more rigorous reasoning. But what we finally have is still ‘appearance’, though in a less pejorative sense than initially.
Thus, ‘real’ or ‘illusory’ are themselves always, ultimately, just appearances. They are themselves, like the objects of consciousness which they evaluate, distinct objects of consciousness. We could say that, there is a bit of the real in the illusory and a bit of the illusory in the real; what they have something in common is appearance. However, these terms lose their meaning if we try to equate them too seriously.
On what basisan appearance may or should be classified as real or illusory is of course a big issue, which needs to be addressed. That is the overall task of logic, to set precise guidelines for such classification. But the first step is to admit the available evidence, the phenomenal world as such: this gives us a data-base.
The Law of Contradiction is an imperative to reject as illusory and not real, any apparent presence together of contradictories. This second law of thought could be stated as ‘Nothing is both A and not-A’, or ‘whatever is, is not whatever it is not’.
We cannot say of anything that it isbothpresent and absent at once:what is present, is not absent. If the world of appearance displays some content with an identity, then it has effectively failed to display nothing. Contradictory appearances cannot coexist, concur, overlap: they are ‘incompatible extremes’.
We can say of something that it ‘is’ something else, in the sense of having a certain relation to something distinct from itself, but we cannot say of it that it both has and lacks that relation, in one and the same respect, at one and the same place and time.
It is evident, and therefore incontrovertible (by the previous law), that appearances are variegated, changing, and diverse. Phenomena have a variety of aspects and are usually composed of different elements, they often change, and differ from each other in many ways. However, for any respect, place and time, we pinpoint, the appearance as such is, and is whatever it is —and not at once otherwise.
The law of contradiction is not a mere rephrasing of the law of identity, note well, but goes one step further: it sets a standard for relegating some appearances to the status of illusions; in a sense, it begins to define what we mean by ‘illusion’. It does not, however, thereby claim that all what is leftover in the field of appearance is real with finality; nor does it deny that some of the leftovers are real (as is assured us by the law of identity).
By the law of identity, whatever appears isgiven some credence: therefore, one might suggest, the coexistence of opposites has some credence. The law of contradiction interposes itself at this point, and says: no, such eventscarry no convictionfor us, once clearly discerned. The first law continues to function as a recognition that there is an apparent contradiction; but the second law imposes on us the need to resolve that contradiction somehow.
The law of contradiction is itself, like anything else, an appearance among others, but it strikes us as anespecially credibleone, capable of overriding the initial credibility of all other considerations. It does not conflict with the message of the law of identity, since the latter is open to any event, including the event that some appearances be more forceful than others. The law of contradiction is precisely one such forceful appearance, an extremely forceful one.
Thus, though the world of appearances presents itself to us with some seeming contradictions, they appearasincredible puzzles — their unacceptability is inherent to them, obvious to us. We may verbally speculate about a world with real contradictions, and say that this position is consistent with itself even if inconsistent with itself. But the fact remains that whenever we are face to face with a specific contradiction (including that one) we are unavoidably skeptical — something seems ‘wrong’.
The way we understand the apparent existence of contradictions is by viewing the world of appearances aslayered, or stratified. Our first impressions of things are often superficial; as our experience grows, our consciousness penetratesmore deeplyinto them. Thus, though each level is what it is (law of identity), parallel levels may be in contradiction; when a contradiction occurs, it is because we are superimposing different layers (law of contradiction). In this way, we resolve the ‘general contradiction’ of contradiction as such — we separate the conflicting elements from each other.
(Note in passing, as an alternative to the metaphor of ‘depth’, which likens consciousness to a beam of light, we also sometimes refer to ‘height’. Here, the suggestion is that the essence of things is more elevated, and we have to raise ourselves up to make contact with it.)
That resolution of contradiction refers to the diversity and change in the world of appearance as due to the perspectives of consciousness. Thus, the appearance of the phenomena we classified as ‘illusory’ is due to the limitations of ordinary consciousness, its failure to know everything. This restriction in the power of consciousness may be viewed as a ‘fault’ of our minds, and in that sense ‘illusion’ is a ‘product’ of our minds. For that reason, we regard the illusory as in some sense ‘imaginary’ — this is our explanation of it.
On a more objective plane, we may of course accept diversity and change as real enough, and explain them with reference to the space and time dimensions, or to uniform and unchanging essences. In such cases, we are able to meet the demands of the law of contradiction without using the concept of ‘illusion’; only when space, time, and respect, are clearly specified, does a contradiction signify illusion.
3.The Law of the Excluded Middle.
The Law of the Excluded Middle is an imperative to reject as illusory and not real, any apparent absence together of contradictories. This third law of thought could be stated as ‘nothing is neither A nor not-A’, or ‘whatever is, either is some thing or is-not that thing’.
We cannot say of anything that it is at once neither present nor absent:what is not present, is absent. If the world of appearance fails to display some content with an identity, then it has effectively displayed nothing. There is no third alternative to these two events (whence the expression ‘excluded middle’): they are exhaustive.
We may well say that some parts or aspects of the world are inaccessible to our limited faculties, but (as pointed out in the discussion of identity) we cannot claim a world beyond that of appearances: the moment we mention it, we include it.
It may be that we neither know that something is so and so, nor know that it is not so and so, but this concerns knowledge only, and in reality that thing either is or is-not so and so. Whatever we consider must either be there or not-there, in the specified respect, place and time, even if we cannot discern things enough to tell at this time or ever. There is an answer to every meaningful question; uncertainty is a ‘state of mind’, without ‘objective’ equivalent.
Moreover,strictly speaking, ‘questions’ are artificial attempts to anticipate undisplayed layers of appearance. As things appear now, if nothing is being displayed,thatis the (current) ‘answer’ of the world of appearances; in the world of appearances there are no ‘questions’. ‘Questions’ merely express our resolve to pursue the matter further, and try to uncover other layers of appearance; they are not statements about reality.
If we choose to,loosely speaking, regard doubts as kinds of assertions, the law of the excluded middle enjoins us to class them at the outset as illusory, and admit that in reality things are definite. Problematic statements like ‘it might or might not be thus’ are not intended to affirm that ‘neither thus nor not-thus’appeared, but that what did appear (whether it was ‘thus’ or ‘not-thus’ — one of them did, for sure) was not sufficiently forceful to satisfy our curiosity.
Even if no phenomenon is encountered which confirms or discredits an idea, there must be a phenomenon capable of doing so, in the world somewhere, sometime. We have to focus on the evidence, and try and distinguish the appearance or nonappearance of that imagined phenomenon.
Thus, the law of the excluded middle serves to create a breach of sorts between the ‘objective world’ and the ‘world of ideas’, and establishes the pre-eminence of the former over the latter. The breach is not an unbridgeable gap, but allows us to expand our language, in such a way that we can discuss eventual layers of appearance besides those so far encountered, even while we admit of the evidence at hand.
Such an artifice is made possible by our general awareness from past experience that appearances do change insomecases, but should not be taken to mean that any given appearancewillchange. It is only the expression of a (commendable) ‘open-mindedness’in principle, with no specific justification in any given case.
What we have done, effectively, is to expand what we mean by ‘appearance’, so as to include future appearance, in addition to appearances until now in evidence. Thus far, our implicit understanding was that appearance wasactual, including present realities and present illusions. Now, we reflect further, and decide to embrace our anticipations of‘possible’appearances as a kind of actuality, too.
Such hypothetical projections are also, in a sense, ‘apparent’. But they are clearly imaginary, inventions of the mind. Their status as appearances is therefore immediately that of ‘illusions’; that is their present status, whatever their future outcome. However, they are illusory with less finality than the phenomena so labeled by the law of contradiction; they retain some degree of credibility.