Logical and Spiritual REFLECTIONS
Book 3. In Defense of Aristotle’s Laws of Thought
Chapter 3. The 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, 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.
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.
 See especially my Ruminations, chapter 9 (“About Negation”).