Saturday 1 May 2004

The Laws of Thought (2004)

From The Philosopher, Volume LXXXXII No. 1 Spring 2004

By James Danaher

Western philosophy to a very large extent has been founded upon laws of thought. We believe that our thinking should strive to eliminate ideas that are vague, contradictory, or ambiguous, and the best way to accomplish this, and thereby ground our thinking in clear and distinct ideas, is to strictly follow Laws of Thought.

Ones like:
  • the Law of Identity (A=A),
  • the Law of Non-contradiction (A does not equal ~A),
  • and the Law of the Excluded Middle (either A or not A but not both A and ~A).
In spite of how dominant these laws of thought have been, they have not been without their critics, and philosophers from Heraclitus to Hegel have leveled powerful arguments against them. But the issue does not seem to be whether the laws are applicable or not, but where and when are they applicable? Certainly, the laws of thought have a place, but what is that place?

Both the laws, as well as opposition to them, can be traced to the Pre-Socratic philosophers. It was Parmenides who first formulated the law of non-contradiction. 
"Never will this prevail, that what is not is."
Plato also refers to this in the Sophist: "The great Parmenides from beginning to end testified . . . 'Never shall this be proved - that things that are not are.'"

It may seem strange that the principle of non-contradiction was not part of a natural way of thinking that had its origins deep in our prehistory, but rather was introduced by Parmenides in the 5th century B.C. Even more surprising is the fact that Parmenides' law of non-contradiction represented a radical break from the Ionian philosophy of nature which preceded it. The Ionian philosophy was based on observation or experience in the ordinary sense. On the basis of such experience, Heraclitus argued that contradictions not only existed but were essential and the basis of a thing's identity: 

"Not only could it be stated that identity is the strife of oppositions but that there could be no identity without such strife within the entity." Heraclitus argued that since things changed, they had to contain what they were not. Only such contradictions could account for change. As Heraclitus says: 
"Cold things grow warm; warm grows cold; wet grows dry; parched grows moist."
In direct opposition to Heraclitus, Parmenides claimed that identity involved the idea of non-contradiction. What made for the difference between Heraclitus and Parmenides was what they respectively believed were the proper objects of thought. For Parmenides, the things we encounter in our experience make for poor objects upon which to fix our thoughts. Indeed, the things we experience are not suited to provide the kind of knowledge that Parmenides, and so many others who were to follow him, wanted. The kind of knowledge they desired was a knowledge that was fixed and certain. Such knowledge would require objects of thought that were equally fixed and certain. Thus, Parmenides settled on the idea of being itself into which all change would collapse.

The Pythagoreans too desired objects of thought that were fixed and certain. For them, mathematics provided those kinds of objects. Plato too sought similar objects of thought and settled on otherworldly forms that were eternal and immutable. With the Platonic forms, as with Pythagorian numbers and Parmenidian being, the laws of thought are certainly applicable. Thus, Plato endorsed the laws of non-contradiction and excluded middle in the Republic when he has Socrates say:
"It is obvious that the same thing will never do or suffer opposites in the same respect in relation to the same thing and at the same time." (Republic 4:436b) 
Of course, Plato was well aware that in order for the laws of thought to work they needed to be restricted, for if left unrestricted they could lead to absurd conclusions. In the Euthydemus, Euthydemus' brother Dionysodorus argues that Socrates must be the father of a dog, since the dog had a father, and Socrates has admitted that he is a father. Since one cannot be a father and not be a father at the same time, Socrates must be the father of the dog. Although Socrates is obviously not the father of the dog, it was not so obvious in Socrates' day where Dionysidorus' thinking went wrong. Thus, Plato attempts to sort out where and when the laws of thought apply and where and when they do not apply.

The restrictions Plato places on the laws of thought (i.e., "in the same respect," and "at the same time,") are an attempt to isolate the object of thought by removing it from all other time but the present and all respects but one. Thus, although we are involved in many relationships, when we think about ourselves relationally, we must restrict our thinking to one relationship, at one time, in order for the laws of thought to be applicable. Thus, it is not only the Platonic forms that are abstract and apart from the world of experience, but any idea to which the laws of thought are to be applied must also be abstracted from the reality of our experience which is multi-relational and multi-temporal.

Like Plato, Aristotle also believed that the laws of thought, in spite of being controversial, were cornerstones of all right thinking. He argues for them in several places (Metaphysics G, 3&4; De Interpretatione 11, 21a32-33; Topics IV 1, 121a22-4; Sophistical Refutations 5, 167a1-6). It is, however, not so much that he argues for them as he sets them in a proper light. That is, he shows were they are appropriate and where they are not appropriate. Basically, what he says is little different from Plato. He argues that such laws apply only to attributes and attributes at a particular time and in a particular respect.
"The same attribute cannot at the same time belong and not belong to the same subject and in the same respect."  
(Metaphysics G, 3,1005b18-20)
By limiting the laws of thought in this way, Aristotle overcomes Heraclitus' claim that identity contains contradictions because the attributes of a thing change over time. By isolating identity in one moment of time, Aristotle abstracts the objects of thought just as Plato had done. Thus, identity is set in a different light than it had been for Heraclitus who understood identity as dynamic and thus involving change and equally contradictions.

But Aristotle also introduces another element to further support the laws of thought. The principle he introduces concerns the way we formulate our concepts or ideas of kinds. According to Aristotle, our idea of a kind or species is best conceptualized by uniting the genus of a species with its differentia or the characteristic that differentiates that species from the other members of the genus. To establish a clear concept of the species "man," we combine the genus "animal" and the differentia or that characteristic which distinguishes man from other animals * for example, that he is rational. Thus, the species "man" is conceptualized as, "rational animal." It may be true that our clearest concepts are those which proceed from, and are members of, a single genus. 
Our desire for clear and distinct concepts has made Aristotle's model for conceptualising species enormously influential in Western thinking. In biology we classify and understand species under a single lineage whereby each concept or idea of a species belongs to only one genus. Every family of living things belongs to only one order, and every order belongs to only one class, and every class to only one phylum and kingdom. Such ordering gives us neat and clear concepts and satisfies our desire to conceptualize things in as simple and clear a way as possible. But the platypus does not fit neatly into a single genus or more precisely into the class designated as "mammal." In fact, many species do not seem to fit such a neat Aristotelian model, and might better be conceived if we understood them to belong to more than a single genus.

This Aristotelian model for conceptualizing species has not only been applied to biological species, but we attempt to organize all of our experience in a similar fashion. In spite of the fact that many of our concepts might be better conceived if we understood them as descending from multiple genuses, the Aristotelian model of concepts which descend from a single genus is deeply entrenched in our thinking. One of the reasons behind its entrenchment is that such a principle allows the laws of thought to work consistently and appear universal. On another model in which concepts are thought to descend from multiple genuses, the laws of thought are not as applicable because, as a member of more than a single genus, a concept could contain contradictory attributes.

Materialism and the Corpuscular Philosophy

With the modern era, a mechanical view of the universe replaced Aristotle's biological paradigm. With such a model, things were no longer organic wholes but composites of parts and, as such, more compatible with an analytic way of thinking that broke things down into ever smaller parts until all contradictions disappear, and the Laws of Thought prevailed. Basic to this mechanical view known as the corpuscular philosophy, was an apparent distinction between the kinds of qualities that we attribute to physical entities. Qualities such as shape, extension, motion, etc. were thought to exist within the objects themselves, while tastes, smells, colors, etc. were said to exist within us. The former kind were referred to as 'primary' and the latter kind 'secondary'.

The explanation the corpuscularians offered was that these secondary qualities were produced in us by the arrangement and motion of the insensible corpuscles which were made up of primary qualities and constituted the internal structure of a thing. So a physical thing like a strawberry, while not actually possessing anything that resembles the taste or smell of the strawberry, does have the power to produce those sensations within us because of the arrangement and motion of the insensible corpuscles that make up the strawberry's internal structure. By contrast, when we perceive that the strawberry is extended, we are perceiving a quality that represents the thing itself, since the strawberry is made up of corpuscles and corpuscles are extended.

Thus, the claim of the corpuscularians was that primary qualities were more real than secondary qualities. Of course, what is meant by "more real" is that primary qualities seem to be more objective than the subjective, secondary qualities. But why should we privilege the objective over the subjective? One reason, perhaps the most important reason, is that the laws of thought are more applicable when subjectivity is removed. Subjectivity certainly undermines the Laws of Thought. While a thing can be sweet and not sweet at the same time, it cannot not be square and round nor in motion and at rest at the same time. Consequently, primary qualities make better objects of thought in the sense that the laws of thought better apply with them than with secondary qualities. What has in fact taken place, however, is that the objects of thought have been made ever more abstract and removed from the reality of the world we actually experience.

The idea of primary qualities, like the objects of mathematics, Plato's otherworldly forms, or Aristotle's idea of species that are members of single genuses, are enormously abstract and artificial notions and not like anything we actually experience. The pure objectivity of primary qualities is something we create rather than experience and we create it for the sake of having clear and distinct objects of thought to which the laws of thought might be consistently applicable. By the 18th and 19th centuries, such abstract notions of objectivity would come under attack from a phenomenological perspective which would take up the Herclitian theme and argue that the phenomenal world of experience is more real than the abstract world we have come to think about.


Berkeley's phenomenalism privileged the world of experience over the abstract world of objective matter which the corpuscularians had introduced. Berkeley thought that abstract ideas of any kind were inconceivable (set out in the Principles of Human Knowledge), and that primary and secondary qualities were inseparably joined in the phenomenal world and could not be separated even in thought.
"I desire anyone to reflect and try, whether he can by any abstraction of thought, conceive the extension and motion of a body, without all other sensible qualities. . . extension, figure, and motion, abstracted from all other qualities, are inconceivable."
For whatever reason, Berkeley did not explore the consequence of his phenomenalism upon the laws of thought. Hegel, however, certainly did. Like Berkeley, Hegel's phenomenalism attacks the idea of abstraction, but Hegel seems to have had more of an understanding of how much the idea of abstraction was at the very base of traditional logic and metaphysics. Hegel seems to understand that the focus of traditional logic was to make "Abstract identity its principle and to try to apprehend the objects of reason by the abstract and finite categories of the understanding." By so doing, traditional logic secured a realm over which the laws of thought could sovereignly rule. 
Once proper objects of thought have been created through abstraction, the laws of thought certainly apply. Hegel would argue, however, that these laws of thought do not apply when the objects of thought are not such abstract entities. Thus, the laws of thought do not universally rule over all thinking but are only universal when the objects of thought are abstracted from the reality of the phenomenal world. If we turn our attention upon the world of experience, "everything is inherently contradictory." Thus, Hegel posits the law of contradiction, rather than the law of non-contradiction.

As it was for Heraclitus, reality for Hegel is something that moves, thus making any fixed, abstract identity impossible. Things are always becoming and so they must contain within themselves that which they are not. Contradiction is the root of all movement and vitality; it is only in so far as something has a contradiction within it that it moves, has an urge and activity.

A little later, he says something that is even more shocking to those who strictly adhere to the traditional laws of thought and imagine them to be the basis of all right thinking. 

"Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this "here", it at once is and is not." This is an obvious contradiction, and the laws of thought would say that something cannot be here and not here at the same time. Of course, what is behind Hegel's statement is the matter of how we conceive of time. If we think of time and motion analytically, and the continuum of time moves from one fixed, analyzable point to another (i.e., t1, t2, t3 . . . ), thus constituting a present or here, then Hegel is certainly wrong. If that is the case, then something is here (e.g., t4) and not any other place. If, however, there are no fixed points on the continuum that is time, and time is continually moving, then it cannot be stopped and analysed without making it something other than what it is. If the nature of time, like motion, defies arrest, then Hegel is right and analytic thinking is not suited to understand such things. To think of time as an ongoing continuum forces us to think contrary to the laws of non-contradiction and excluded middle, and understand that something is both here and not here at the same moment.

If motion defies the traditional laws of thought, then all living things violate the laws of thought in so far as they are in constant motion * not in the sense that they experience constant local motion but in the sense that all living things experience perpetual internal motion. This internal motion of all living things prevents them from having any fixed, analyzable point of identity.
"Abstract self-identity is not as yet a livingness....  Something is therefore alive only in so far as it contains contradictions within it." 
Hegel even attacks the law of identity and claims that the law of identity says very little in itself.  The fact that A = A is no more than a tautology and has little meaning.  It tells us almost nothing about the identity of a thing.   The only way a thing truly takes on identity is through its otherness or what it is not.  What a thing is not is as necessary to the identity of a thing as what it is in that what it is not is what gives boundaries, definition, and meaning to a thing.  Thus, its otherness must be contained within the very identity of the thing. 
What is at the base of all that Hegel has to say is a logic that is synthetic rather than analytic.  With a synthetic logic which joins things into ever greater wholes rather than analyzing them into ever smaller parts, the Laws of Thought are not the universal principles they are with analytic thinking.  With a synthetic logic that examines wholes rather than parts, contradictions are natural and to be expected.  The way to eliminate contradictions is to employ an analytic logic which divides things into ever smaller parts until the contradiction disappears.  When Plato and Aristotle qualify the law of non-contradiction and say "in the same respect," and "at the same time," what they are doing is breaking a thing down into its parts.  If we focus on ever smaller parts, we can eventually eliminate all contradictions and thus preserve the law of non-contradiction and the law of the excluded middle.  When, however, we deal with the whole, rather than the parts, we are treating all the respects or parts together and then we certainly may encounter contradictions and the truth is often both/and rather than either/or.
When we say that life is full of joy and sorrow, we can eliminate that contradiction, or any such contradiction, by analyzing life and dividing it into joyous parts and sorrowful parts.  That is, in one respect, it is joyous and in another respect it is sorrowful.  If, however, we leave life (or anything else) whole and do not analyze it into this respect or that respect, we see myriads of contradictions because that is the nature of the reality in which we live.  We have been taught to think analytically about abstracted parts of our experience in order that the laws of thought can be neatly applied, but that is only one way of thinking.  We can also think about wholes rather than parts and when we do, the laws of thought do not always apply.
This does not mean that there is no place for analytic thinking and the laws of thought.  Analytic thinking is a mode of thought we use all the time.  The problem lies in the fact that Western intellectual history has been intent upon creating an understanding that is founded upon universal laws, and, in order to create such universal laws, we have attempted to eliminate all objects of thought to which such laws do not universal apply.  This, however, is irrational since there obviously are dynamic and holistic objects of thought to which the laws of thought do not universally apply.
Twentieth century science has discovered the bicameral nature of the human brain, and although pop psychology might be too quick to draw hard and fast lines between the two hemispheres of the brain and assigns analytic thought to the one and synthetic thought to the other, there certainly is something to the fact that the physiology of our brains allow us to think in different ways.  Analytic thinking, based upon one hemisphere of the brain, has dominated in the West.  Thus, it is no wonder that the laws of thought seem so absolute to so many. Yet, to strictly apply the laws of thought to all of our thinking is perhaps to use only half our wits. 

Address for correspondence:

James P. Danaher, Ph.D.
Professor of Philosophy
Head, Department of Philosophy 


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  3. "Certainly, the laws of thought have a place, but what is that place?"

    We cannot determine this place from within the formalism under study. We do not know how to translate the laws of another formalism into the field of the formalism under study. We cannot formulate the scope of the investigated formalism.

    The problem has an elegant solution through a trivial mathematical model of contradiction. Discussed laws of thinking work locally. but they are not reasonable in general. Logic based on a contradictory formalism is strict, defines itself, proves itself and demonstrates the scope of the laws of thought under discussion.

    A contradictory formalism describes a model of the whole. The properties of the model of the whole turn out to be the properties of the material part of reality. I amresearching this model in practice. She works.


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