The Laws of Thought

1.     Ontological Status of the Laws

Discussion of the laws of thought inevitably arrives at the question: are these ontological or epistemological laws, or both; and if both in what sequence? Furthermore, what is their own ontological status – i.e. where do they ‘reside’, as it were? Are they ‘out there’ somehow, or only ‘in our minds’?

As my thought on the issue has evolved over the years[1], I am now convinced that the traditional term “laws of thought” is accurate, in that these statements are primarily imperatives to us humans on how to think about reality, i.e. how to ensure that we cognitively treat the givens of appearance correctly, so that our ideas remain reasonably credible possible expressions of reality and do not degenerate into delusions.

Why? Because Nature can only posit; and so ‘negating’ depends on Man. That is to say, the world process is always positive; negation involves a particular relation between a conscious being and that presentation. For negation to occur, a conscious being has to project and look for something positive and fail to find it; otherwise, all that occurs is positive.

Thus, when we state the laws of non-contradiction and of the excluded middle, formally as “X and not X cannot both be true” and “X and not X cannot both be untrue”, we mean that such claims (i.e. ‘both true’ or ‘both untrue’) cannot reasonably be made within discourse. We mean that ‘X and not-X’, respectively ‘not-X and not-not-X’, cannot correctly be claimed as known or even as reasonably opined.

Conjunctions of (positive or negative) contradictories are thus outside the bounds of logically acceptable discourse. These two laws of thought together and inseparably effectively define what we naturally mean by negation. Note well, ‘middles’ between contradictories are as unthinkable as coexisting contradictories.

Note that the law of identity is also tacitly involved in such definition of negation, since before we can understand the logical act of negating, we must grasp the fact of positive presence. So, it is not just the second and third laws that define negation, but strictly speaking also the first.

Such definition is, needless to say, not arbitrary or hypothetical. Were someone to propose some other definition of negation (e.g. using the law of non-contradiction alone, or some other statement altogether), this would only produce an equivocation – the natural definition with reference to the three laws of thought would still be necessary and intended below the surface of all discourse, however willfully suppressed.

From this it follows, by an extrapolation from logically legitimate thought to reality beyond thought, that these laws of thought (or, identically, of logic – ‘logic’ meaning ‘discourse’ by a thinker) are also necessarily laws of reality.

Words are symbols, and symbols can be made to do what one wills, because they are per se not in fact subject to the laws of thought. That is to say, mental gymnastics like placing the symbol X next to the symbol not-X are indeed feasible, but that does not mean that the things the symbols symbolize can equally well be conjoined.

To label an observed illusion or a deliberate fantasy as ‘real’ does not make it in fact real. We can easily verbally imagine a ‘reality’ with non-identity, contradictions and inclusions of the middle, but we cannot actually conjure one.

2.     The Need for a Conscious Subject

As for the status of the laws of thought themselves: being products of reason, their existence depends on that of a conscious – indeed, rational – subject. All particular acts of reasoning – such as negation, abstraction, measurement, classification, predication, generalization, etc. – depend for their existence on some such rational subject (e.g. a man).

Take away all such subjects from the universe, and only positive particular things or events will remain. Without an act of negation, no mixing of or intermediate between contradictories occurs in thought; all the more so, they cannot occur outside thought. Similarly, with regard to abstraction and other acts of the reasoning subject.

Concepts like similarity, difference, uniformity, variety, continuity, change, harmony, contradiction, and principles like the laws of thought, being all outcomes of such ratiocinative acts, are similarly dependent for their existence on there being some appropriately conscious subject(s).

These concepts and principles are, we might say, inherent in the world in the way of a potential; but without the involvement of such a subject, that potential can never be actualized.

These concepts and principles depend for their existence on there being conscious subjects to form them – but their truth or falsehood is not a function of these subjects. Their occurrence is dependent, but the accuracy of their content when they occur is a different issue. It is not subjective and relative, but on the contrary objective and absolute.

It is important not to draw the wrong inference from the said existential dependence, and to think it implies some sort of relativism and subjectivism (in the most pejorative senses of those terms) as regards issues of truth and falsehood.

No: the ‘reasonableness’ of our basic concepts and principles is the guarantee of their truth. To suggest some other standard of judgment, or the equivalence of all standards of judgment, is to tacitly claim such other standard(s) to be somehow ‘reasonable’. A contradiction is involved in such an attitude. Of course, you are free to propose and accept contradictions, but you will have to pay the cognitive and other consequences. As for me, I prefer to stand by and rely on what is evidently reasonable.

3.     Fuzzy Logic

In some cases, X and notX are considered not to be contradictory, because the term or proposition X is too vague. If precisely what things X refers to is unclear, or if the exact boundaries of some individual thing labeled X are uncertain, then obviously the same can be said for the negative complement ‘not X’ (see diagram further on). In such cases, the terms or propositions involved are simply problematic.[2]

It is easy to see how such realization can lead to a general critique of the human rational act of naming, and to a philosophy of Nominalism. For, if we observe our concepts carefully, we must admit that they are always in process – they are never fully formed, never finalized. Our ordinary knowledge is predominantly notional, tending towards precise conception but never quite attaining it. Thus, the meaning of words (or even of wordless intentions) is in flux – it is becoming rather than being.

This is not a merely epistemological critique, but one that has ontological significance. What is being said here is that things, the objects of our consciousness (be they objective or subjective) are difficult, if not impossible, to precisely pin down and delimit. This is true of concrete individuals and of abstract classes. It is true of matter (e.g. where does the body of a man end: if I breathe air in or out, or swallow water or spit it out, at what stage does the matter entering or exiting become or cease to be part of ‘my body’?), and it is true of mind and of soul (who knows where their respective limits are?).

Ultimately, we realize, everything is one continuum, and the divisions we assume between things or classes are ratiocinative and intellectual interpositions. We cannot even truly imagine a fine line, a separation devoid of thickness, so how can we claim to even mentally precisely separate one thing from another? All the more so in the physical realm, such division is impossible, given that all is composed of continuous and endless fields.

Another critical tack consists of saying that all our experience (and consequently all our conceptual knowledge) is illusory, in the way that a dream is illusory (compared to awake experience). In a dream world, X and not X can apparently both coexist without infringing the law of non-contradiction. Distinctions disappear; opposites fuse into each other.

But this is only superficially critical of our ordinary knowledge. For what is said to coexist here are ‘the appearance of X’ and ‘the appearance of not X’ – and not ‘X’ and ‘not X’ themselves. We have symbols, or stand-ins, or effects, instead of the objects themselves. So, this is nothing that puts the law in doubt, but rather a viewpoint that by its own terminology (reference to illusion) confirms adherence in principle to that law.

Such reflections lead us to the idea of fuzzy logic, as opposed to definite logic. The difference is illustrated in the following diagram:

Figure 20.1      Definite and Indefinite terminology.

Aristotle’s three laws of thought are aimed at a “definite logic” model – in this model, terms and theses are in principle clearly definable and knowable; or at least, this is the assumption in most cases, though in a minority of cases there might be some measure of temporary vagueness and doubt. But this ideal is in practice rarely met, and we should rather refer to a “fuzzy logic” model – wherein the assumption in most cases is that limits are chronically unclear and hard to establish with certainty, though exceptions to this rule must be acknowledged for the sake of consistency.

Ordinarily, our reason functions in a self-confident manner, from conviction to conviction, unfazed by the changes in our ‘utter convictions’ that in fact occur over time. In other words, we lay the stress on what we (think we) know, and minimize what we consider still unknown or the errors we made in the past. This is the approach of definite logic, an essentially ‘deductive’ approach. The idea of a fuzzy logic is that we ought to, on the contrary, at the outset acknowledge our cognitive limitations and the ongoing flux of knowing, and opt more thoroughly for an ‘inductive’ approach.

According to this view, the logical perfection presupposed by Aristotle is largely mythical. Our concepts, propositions and arguments are, in practice, usually exploratory, tentative, approximating, open-ended with regard to referents, open to change, of uncertain pertinence and truth, and so forth. Our rational faculty works by trial and error, constantly trying out different overlays that might fit a momentarily glimpsed reality, then noticing an apparent mismatch trying out some more adjusted overlay, and so on without end.

Things are rarely quite the way we think of them, and yet our thought of them is not entirely wrong. Hence, we might well say that it is not correct to say that the referents of X fit exactly what we mean by ‘X’; and it is not correct to say that they do not all or wholly fit in. Hence, it might be said that certain things are both X and not X, and neither X nor not X – without really intending to imply any contradiction, but only in the way of a reminder to ourselves that we are functioning in shifting sands.

Such a logical posture does not really constitute a denial of the laws of thought. They continue to help us make sense of things. Their precision helps us sort out the vagueness and uncertainty we actually face in practice. They give us an ontological and epistemological ideal we can tend to, even if we can never hope to fully and permanently match it.

4.     Stick to Logic

In the light of the aforementioned difficulties, some logicians and philosophers are tempted to give up on all rational knowledge, and more specifically the laws of thought. However – and this is the point I am trying to make here – this would be a tragic error. The error here is to think that we humans can navigate within the sea of phenomena and intuitions without the guiding star of the laws of thought. Even if in particular cases these laws are often hard to apply decisively, they help us do our best to make sense of the world of appearances we face.

We have to stick with logic. It provides us with a minimum of firm ground in the midst of the shifting sands of experience and conception. Even if it is only an ideal, a theoretical norm, its importance is crucial. Without logic, we have no way to sort out changing impressions and deal with the practical challenges of our existence. Is that not the very definition of madness, insanity?

Nevertheless, sticking to logic should not be taken to signify rigid conventionality, or fearful closed-mindedness, or similar excesses of ‘rationalism’. Sticking to logic does not exclude enlightened consciousness, flowing with the current of life, having faith, and similar liberating attitudes. Logic is a tool, not an end in itself. To give up a useful tool is stupid; but it is also stupid not to know when to put down the tool.

There is a stage in the life of the spirit when logical ifs and buts become irrelevant, or even disturbing, and it is wise to just be.