We began our study by presenting the laws of thought — the Laws of Identity, of Contradiction, and of the Excluded Middle — as the foundations of logic. We can see, as we proceed, that these first principles are repeatedly appealed to in reasoning and validation processes. But in what sense are they ‘laws’?
a.Many logicians have been tempted to compare these laws to theaxiomsof geometry, or the top postulates of natural sciences. According to this view, they are self-consistent hypotheses, which however are incapable of ultimate proof, from which all other propositions of logic are derived.
There is some truth to this view, but it is inaccurate on many counts. The whole concept of ‘systematization’ of knowledge, ordering it into axioms and derivatives, is itself a device developed and validated by the science of logic. It is onlyex post factothat we can order the information provided by logic in this way; we cannot appeal to it without circularity. If logic was based on so tenuous a foundation, we could design alternative logics (and some indeed have tried), just as Euclidean geometry or Newtonian mechanics were replaced by others.
Logic is prior to methodology. The idea that something may be ‘derived’ from something else, depends for its credibility on the insights provided by the ‘laws of thought’. The ‘laws of thought’ ought not to be viewed as general principles which areappliedto particular cases, because the process of application itself depends on them.
Rather, we must viewevery particular occurrenceof identity, contradiction, and excluded-middle, asby itself compelling, an irreducible primary independently of any appeal to large principles. The principles are then merely statements to remind usthatthis compulsion occurs; they are not its source. This means that the ‘laws of thought’ are not general principles in the normal sense, but recognitions that ‘there are such events’. The science of logic is, then, not a systematic application of certain axioms, buta record of the kind of events which have this compelling characterfor us.
Note this well.Eachoccurrence of such events is self-sufficiently evident; it is only thereafter that we can formulate statements about ‘all’ these events. We do not know what to include under the ‘all’ beforehand, so how could we ‘apply’ the laws to anything? These laws cannot be strictly-speaking ‘generalizations’, since generalization presupposes that you have some prior datatogeneralize.
Thus, we must admit thatfirstcomes specific events of identity, contradiction and excluded-middle, with a force of their own, then we can say ‘these and those arethe kinds ofsituations’ where we experience that utter certainty, and only lastly can weloosely-speakingformat the information in the way of axioms and derivatives.
Nevertheless, it remains true that the laws of thought have a compelling character on their own. There is no way to put these laws in doubt, without implicitly arousing doubt in one’s own claim. Sophisms always conceal their own implications, and tacitly appeal to the laws of thought for support, to gain our credulity. We could, therefore, equally say that the principles as units in themselves are entirely convincing, with utter finality — provided wealsosay that every act of their ‘application’ is likewise indubitable. It comes to the same.
However, the previous position is more accurate, because it explains how people unversed in the laws of thought, can nonetheless think quite logically — and also how we can understand the arguments here made about the laws of thought. The inconsistency of denials of the laws of thought is one instance of those laws, and not their whole basis.
b.What, then, is this ‘compulsion’ that we have mentioned? It is evident that people are not forced to think logically, say like physical bodies are forced to behave in certain ways. This is given: we do make errors, and these sometimes seem ‘voluntary’, and sometimes accidental. In any case, if thought was a mechanistic phenomenon, we would have no need of logical guidelines. We may only at best claim that wecan and should, and sometimes do, think in perfect accord with these laws.
The answer to this question was implicit in the above discussion. It is or seems evident that things do present themselves and that they do have certain contents (identity), and that these presentations are distinct from their absences (contradiction), and that there is nothing else to refer to (excluded-middle). Because these statements concern appearances as such, it is irrelevant whether we say ‘itisevident’ or ‘itseemsevident’.
The concepts of reality and appearance are identical, with regard to the phenomenal; the concept of illusion is only meaningful as a subdivision of the phenomenal. These laws are thereforealwaysevident, whether we are dealing with realities or illusions. We can wrongly interpret or deliberately lie about what we ‘see’ (if anything), butthatwe ‘saw’ andjust whatwe ‘saw’ is pure data. Thus, the ‘compulsion’ is presented to us an intrinsic component of the phenomenal world we face.
The practical significance of this can be brought out with reference to the law of contradiction. We are saying, in effect, that whatever seems contradictory, is so. This statement may surprise, since we sometimes ‘change our minds’ about contradictions.
To understand it, consider two phenomena, say P1 and P2, in apparent contradiction, call this C1. One way to resolve C1, is to say that one or both of P1 and P2 are illusory. But we might find, upon closer inspection, that the two phenomena are not in contradiction; call this noncontradiction C2. So we now have two new phenomena, C1 and C2, in apparent contradiction; call this new contradiction C3.
The question is, does C3 imply that one or both of C1 and C2 are illusory? The answer is, no — what happened ‘upon closer inspection’ was not a revision of C1, but a revision of P1 and/or P2. So that in fact C2 does not concern exactly the same phenomena P1 and P2, but a slightly different pair of phenomena with the same names.
Thus, C1 and C2 could never be called illusory (except loosely speaking), because they were never in conflict, because they do not relate the same pair of phenomena. Nor for that matter may C3 be viewed as now erroneous, because the pair of phenomena it, in turn, related have changed.
Which means that our ‘intuition’ of contradiction is invariably correct,for exactly the data providedto it. A similar argument can be made with regard to other logical relations. The phenomena related may be unclear and we may confuse phenomena (thinking them the same when they are different) — but, at any level of appearance, the logical relation between phenomena is ‘compulsively evident’, inflexibly fixed,given.
In other words,among phenomena, logical relations are one kind which are always real; in their case, appearance and reality are one and the same, and there are no illusions. The laws of thought are presented as imperatives, to urge us to focus on and carefully scrutinizethe phenomena related, and not to suggest that thelogicalintuitions of thought are fallible, once the effort is made to discern the relation.
This is not a claim to any prior omniscience, but a case by case accuracy. As each situation arises, its logical aspects are manifest to the degree that we inspect things clearly. Note well, we do not need to knowhowthe intuition functions, to be able to know and provethatit functions well. We have called it ‘intuition’ to suggest that it is a direct kind of consciousness, which may well be conceptual rather than perceptual, but these descriptive issues are secondary.
Thus, with regard to the laws of thought, we have no ground for wondering whether they are animal instincts imposed by the structure of the mind, or for wondering whether they control the events external to it as well. In either case, we would be suggesting that there is a chance that they might be illusory and not real. If we claim that the mind is distortive, one way or the other, we put that very claim in doubt.
The mind is doubtless limited. It is common knowledge that mental conditions, structural or psychological or voluntary, caninhibitus from comparing phenomena with a view to their logical relation — but that does not mean that when the elementsarebrought together, the comparison may fail.
Nervous system malfunctions, personality disorders, drunkenness, fatigue — such things can only arrest, never alter these intuitions. As for evasions and lies, we may delude ourselves or others, to justify some behavior or through attachment to a dogma — but these are after the fact interventions.
The laws of thought relate to the credibility, or trustworthiness, of phenomena. They clarify things in three stages. At the identity level, appearances are acknowledged and taken as a data base. At the contradiction level, we learn to discriminate clearly between real and illusory appearances. At the excluded-middle level, we introduce a more tempered outlook, without however ignoring the previous lessons. More specifically, their functions are as follows:
The first law assigns a minimal credibility to any thought whatsoever, if only momentarily; the evidence, such as it is, is considered. If, however, the ‘thought’ is found to consist of meaningless words, or is overly vague or obscure — it is as if nothing has appeared, and credibility disappears (until and unless some improvement is made). To the extent that a thought has some meaning, precision, and clarity, it retains some credibility.
The second law puts in doubt any thoughts which somehow give rise to contradictions, and thereby somewhat enhances the credibility of all thoughts which pass this test. In the case of a thought which is self-inconsistent (whether as a whole or through the conflicts of its parts), its credibility falls to zero, and the credibility of denial becomes extreme. In the case of two or more thoughts, each of which is self-consistent, but which are incompatible with each other, the loss of credibility is collective, and so individually less final.
The third law sets bounds for any leftover thoughts (those with more than zero and less than total credibility, according to the previous two laws): if special ways be found to increase or decrease their credibilities, the overall results cannot in any case be such as to transgress the excluded-middle requirement (as well as the no-contradiction requirement, of course). As we shall see, the processes of confirmation and discrediting of hypotheses are ways logic uses to further specify credibilities.
We see that, essentially, the law of identity gives credence toexperience, in the widest sense, including concrete perceptions and abstract conceptual insights. The law of contradiction essentially justifies the logical intuitions ofreason. The law of the excluded-middle is essentially directed at the projections of theimagination. This division of labor is not exclusive — all three laws come into play at every stage — but it has some pertinence.
The credibility of a phenomenon is, then, a measure of how well it fits into the total picture presented by the world of appearances; it is a component of phenomena, like bodies have weight. This property is in some cases fixed; but in most cases, variable — an outcome of the interactions of phenomena as such.
The laws of thought are, however, only the first steps in a study of credibility. The enterprise called logic is a continual search for additional or subsidiary norms. Logic theory develops, as we shall see, by considering various kinds of situations, and predicting the sorts of inferences which are feasible in each setting.
More broadly the whole of philosophy and science may be viewed as providing us with more or less rough and ready, practical yardsticks for determining the relative credibility of phenomena. However, such norms are not of direct interest to the logician, and are for him (relatively speaking) specific world views. Logic has to make do with the two broadest categories of reality and illusion — at least, to begin with.
Every phenomenon appears to us with some degree of‘credibility’, as an inherent component of its appearance; this is an expression of the law of identity. That initially intuitive credibility may be annulled or made extreme, through the law of contradiction; or it may be incrementally increased or decreased, by various techniques (yet to be shown), within the confines of the laws of contradiction and of the excluded middle.
Thus, credibility is primarily an aspect of the phenomenal world, and a specific phenomenon’s degree of credibility is a function of what other phenomena are present in the world of appearances at that stage in its development. Because phenomena interact in this way, and affect each other’s credibilities, credibility may be viewed as a measure of how well or badly any phenomenon ‘fits in’ with the rest.
‘Reality’ and ‘illusion’ are just the extremes of credibility and incredibility, respectively; they are phenomena with that special character of total or zero force of conviction. We cannot refer to a domain beyond that of appearances, for good or bad, without thereby including it within the world of appearances.
How do we know that all appearances must ultimately be real or illusory? How do we know thatmediancredibility cannot be a permanent state of affairs in some cases, on a par with the extremes of credibility and incredibility? We answered this question, in broad terms, in our discussions on the laws of thought, as follows. More will be said about it as we proceed.
Reality and illusion are a dichotomy of actual appearances: for them, whatever is inconsistent is illusory, and everything else is real enough. Median credibility only comes into play when we try to anticipate future appearances, but has no equivalent in the given world. In the actual field of concrete and abstract experiences, things have either no credibility or effectively total credibility; it is only through the artificial dimension of mental projections that intermediate credibility arises.
Knowledge is merely consciousness of appearances; the flip-side, as it were, of the event of appearance. Viewed in this perspective, without making claims to anything but the phenomenal, knowledge is always a faithful rendering of the way things appear. We may speak of knowledge itself as being realistic or as unrealistic or as hypothetical, only insofar as we understand that this refers tothe kind ofappearance it reflects. These characterizations refer primarily, not to knowledge, but to its objects.
The difference between knowledge (in its narrower sense of, knowledge of reality) and opinion (in the sense of, the practically known), is thus merely one of degree of credibilitymanifested by their objects(at that time); we cannot point to any essential, structural difference between them. However, this distinction is still significant: it matters a lot that the objects carry different weights of conviction.
Changes or differences in appearances and opinion are to some extentexplainedby reference to variations in our perspective, and breadth and depth of consciousness. But this explanation does not annul the primacy of phenomena, in all their aspects.
In practise, median credibility is often not patiently accepted, but we use our ‘wisdom’ to lean one way or the other a bit, according to which idea seems to ‘hang together’ the best. But a contrary function of wisdom is the ability to see alternatives, or the remote possibility of suggested alternatives, and thus keep an open mind. The intelligent man is able to take positions where others dither, and also to see problems where others see certainties.
I would like to here mention in passing, without going into details, that work has been done by some logicians, in clarifying the logical properties of belief (or opinion) and knowing.
The logic of belief is concerned with the implications of propositions such as ‘S believes that P’, where S is a subject of consciousness and P is any proposition. Belief, disbelief, and uncertainty are subjectively given: they are facts immediately accessible to the subject, though they may be wrongly remembered or dishonestly reported. There are also iterative forms to consider, like ‘X believes that Y believes that Z’.
The following are some of the formal issues in this field. Mutual oppositions: believing something does not imply disbelieving its contradictory, since people sometimes do (however ‘illogically’) believe both a thesis and its contradictory; therefore, disbelieving and not-believing are not identical. Also, relationships to ‘alethic’ propositions: believing something does not imply that it is true, and the true may be disbelieved.
The logic of knowing may similarly be investigated, for forms like ‘S knows that P’. These topics are not unrelated, since knowing is taken to imply believing (ordinarily, though sometimes we resist), even if we believe some things without the degree of certainty which we qualify as knowing (or perhaps with reference to other standards of judgment). The distinction between conscious awareness and ‘tacit knowledge’ has to be considered.
Knowing is often regarded as based on more rigorous methodology than belief, and hence effectively implying (at least contextual) truth; whereas belief may be groundless or even contrary to reason. Knowing implies some effort of review and control of belief, with reference to logical standards of some sort. If one has trained oneself in logic, avoided all laziness, and tried to be honest, then as far as that subject is concerned his or her belief has become knowledge. For that subject now, though not necessarily at some other time or for other subjects, this is equivalent to the ideal of truth.
Belief, knowing and alethic truth are three parts of the same curve: truth is the ‘vanishing point’ toward which belief and knowing tend. Belief is more inertial, more affected by emotional forces, like peer group pressure or psychological factors. Knowing involves willfully freeing one’s mind of such prejudices and influences, but is still a function of one’s intelligence, logical skills, research efforts, the limitations of one’s cognitive faculties.