Are the ‘Laws of Thought’ Merely Theories?
Posted on: April 3, 2016 /
You might wonder about the title of this talk. I know I did. Titles are important. To illustrate that, I’ll start with a story told me by the late Jim Mac Adam, my tutor and mentor as a Trent student. Jim MacAdam told of a scene from his time as a student at the University of Edinburgh. He had the opportunity to attend a lecture by a great theologian and scholar of Hegel, coming from the Vatican – I don’t remember the name, perhaps it was Karl Rahner. This man was known to be of exceeding powerful intellect and quite formidable. The scholar swept into the hall – grand and magisterial. He appeared at the lectern like a bird of prey, no pun intended. He stated the title of his lecture: “Being and Non-Being in Hegel’. Immediately five hands shot up. Clearly surprised, the scholar recognized one of the students. “Surely you mean “Being and Not-Being?”; but another student stood and stated “No, of course not, it should be formulated “Being and its opposite”. In no time at all, a debate erupted within the audience, on what the title of the lecture should be. After a time, the exchanges became quite heated, with insults and epithets. Student Mac Adam thought he should leave. The Vatican scholar, in high dudgeon, thundered up the aisle, stopped, grabbed him by the shirt front and roared: “What’s the greatest work of philosophy ever written?’ Before our rather terrified student could respond, the scholar barked: “Alice in Wonderland!” and left the hall.
Here are the lessons learned. First, titles are important. Second, no questions till the end.
Here’s what I propose to talk about. I would like to explore the stresses and strains – from various sources – on what are considered the classical laws of thought. So I will start with some important points I see in the laws, then talk about some theories in quantum physics which seem to question the accuracy, indeed the applicability, of those laws. Towards the end, I will speculate about worlds where the laws do not seem to apply.
Laws of Thought
We can state the first three classical laws of thought as follows:
- Whatever is, is (A=A)
- Nothing can both be and not be (NOT(A = NOT-A))
- Everything must either be or not be (FOR ALL A: A OR ~A)
Let us start with the first law, known as the law of identity. One basic formulation is “A=A”, which sounds reasonable to say, although it doesn’t seem to tell us very much. But the next time you hear someone say “It is what it is” you don’t need to conclude that that person is brain dead; he or she has just stated the law of identity. Of course, they may still be brain dead …
To me, the law of identity is primus inter pares of the three laws. All three stand together but it seems to me that number 2 and number 3 are unintelligible without number 1. There must be an ‘A’ such that there can be a ‘not-A’ let alone an ‘either A or not-A’. I don’t mean to diminish the importance of the ‘not-A’; non-being, not-being, un-being are major concepts. I’m mostly talking about the importance of the core concept of identity; if something exists, it has an identity.
Simple though it is, the law is very important for any kind of discourse, especially philosophical. If we cannot name things in a consistent way, then communication becomes very difficult. If I start talking about pizza and then talk about driving it around the block, you might doubt my sobriety, my sanity, my coherence, or at the very least my table manners. Aristotle says our reason would be “annihilated” without the law of identity.
 (Bertrand Russell, 1912)
That said, the law of identity has had less than universal acceptance. You remember Heraclitus, described by Plato as saying “you could not step twice into the same river”. No pun intended, Heraclitus had a much more fluid idea of identity – change was constant, identity was indefinite. In fact, he saw opposites in the same thing: each of us is at various times waking and sleeping, for example. 2500 years later, a similar challenge was made by former US President Clinton, who when asked about his affair with an intern, said “It depends upon what the meaning of the word ‘is’ is”. His point, while doing his best to dodge the question, was that the word ‘is’ might apply as a general description of something – the affair – that had happened in the past or a specific description of something happening at that particular moment.
Aristotle focused on the aspect of the particular object and the particular moment to defend the idea of consistent identity: “The same attribute cannot at the same time belong and not belong to the same subject and in the same respect.”
In focusing on ‘the river’ at a particular moment and circumstance, Aristotle makes an abstraction from reality, just as Plato did describing The Forms. The abstraction could be considered as defensible in that it would indeed be difficult to describe a river as it was flowing, or a tree as it was swaying in the breeze. In each case, the object of the description is changing in space and time, so you need to take space and time out of the equation in order to have a description of an object which has a fixed identity.
One reason to dispute this was offered by a certain Mr. Hegel – imagine George Friedrich Hegel and William Jefferson Clinton in the same example – what have I done? – Hegel made a very reasonable observation that the rules which apply to abstractions might well not apply to events and things in the material (non-abstracted) world.
For our understanding of identity, we need the keep in mind the idea of “the particular moment”. And we also need to note that it is necessary to make an abstraction to maintain this law. All of this will come up later.
 Plato Cratylus 402a
 Metaphysics G, 3,1005b18-20
 James Danaher, The Laws of Thought, The Philosopher, Volume LXXXXII No. 1
Let’s transition from the law of identity. We observe that the ‘other’ to ‘what is’, is in fact quite important to our understanding of what is. “A=A” tells us only about the characteristics of A. Suppose ‘A’ is a red box, all that we have is a “red box = a red box”. If there were only red boxes in the world this would tell us nothing. But there are blue boxes, and green spheres, and hot pink polygons. We can separate out the red boxes precisely because there are other objects of different shape and structure. The ‘other’ – what the red box is not – helps us understand what ‘is’ means. This argument states that if we are to understand ‘A’ we must also understand ‘not A’. And that is good as saying that contradiction has a degree of necessity in order to describe ‘identity’ which was the first law. There is also an argument that non-contradiction is essential to our understanding of language and meaning, both in argument and in the physical world. We must assume that “opposite assertions cannot be true at the same time”, for if we do not then two conflicting states – being/non-being, up/down, in/out, etc. – could be present at the same time and space. In any case, it would be rather difficult to mount a logical attack on the law, since it the law is itself required to assert its denial.
One impressive defence of the law could be classified under the heading of ‘Argument by Intimidation’. Here are the words of Avicenna:
“Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.”
Apparently the success of this particular demonstration requires the destruction of the subject.
Speaking of destruction of the subject, I might have been able to demonstrate a contradictory instance in earlier days. I once owned and wore a wonderful iridescent tie, which was bright red in one light, and bright blue in another. I would have brought this today as proof, but a woman friend found it unacceptably hideous, and destroyed it.
Actual contradictory instances are not all that common – and not all that long-lasting. We use a special word – oxymoron – to describe contradictory conjunctions: ‘bittersweet’ is one, “aging yuppie” is another.
Were we to deny non-contradiction, we would accept that someone or something could exist and not exist at the same time. Did you hear a “meow”? Schrödinger’s cat! Oh pretty kitty, we will come back to you.
I might make a passing reference to Mr. Hegel again, this time without Bill Clinton. I try to be very careful with Hegel, as there are vigorous debates about his actual meaning – as I described in my little story at the beginning. But I think it’s fair to say that ‘contradiction’ was almost an underpinning for his dialectic. The change from something that is to something that is not takes ‘time’, measured as the interval between events. Time is an abstraction from change. I’m not going to dig myself too much further into this bottomless pit, save to observe that for both Heraclitus and Hegel, Plato and Aristotle fudged the argument about identity and non-contradiction, by insisting on fixed temporal and spatial coordinates.
I won’t spend a great deal of time on the law of the excluded middle. In giving it short shrift, I suppose I am proving that the law is indeed excluded. The law basically says that things need to be one thing or another. This law is an essential part of reasoning, but it seems a derivative from the laws of identity and non-contradiction. Nonetheless, the importance of the law will become clear when we wrestle with the idea of the same thing both existing and not, apparently at the same time. Our friend Schrödinger’s cat will make its appearance and non-appearance known or unknown at that time.
I wonder whether a large part of the problem I have in reconciling the laws of thought with the precepts of quantum physics started with the theory of relativity. I’m not thinking of any advanced part of it, but just the notion of special relativity. According to special relativity, the measurement of time and distance depends on the position of the observer.
If time becomes relative to the observer, then the underpinnings of the “this time, this space” defence against the argument of Heraclitus start to get a bit shaky. Surely it is difficult to make an absolute assertion about identity at a fixed time, when time itself is relative to the position of the person making the assertion. You need to be confident about the stability of the concepts ‘space’ and ‘time’ to insist on their use as pillars buttressing the identity argument.
Our confidence is further shaken by the theory, apparently validated through observation, that space-time can be altered by mass, that space-time can be curved. And then we’re on our way down the rabbit hole into quantum mechanics or quantum physics.
Some people argue that the theories and findings of quantum physics are, at best, inconsistent with the laws of thought. The identity of subatomic ‘things’ is not fixed: a particle is a wave. ‘Things’ pop in and out of existence depending on whether you look at them: here kitty, here kitty. ‘Things’ can be one thing and its own other.
To show this happening, I will do my best to describe the salient points of what’s called the double slit experiment. According to the late physicist Richard Feynman this experiment “contains all the mystery of quantum mechanics”. I regret I am not a quantum physicist so I apologize for oversimplifications. But I do think I’ve got the point of it.
We fire a photon – a particle – of light through a wall with two subatomic slits in it; behind that wall is a detector of photons. We might expect that that photon would pass though one slit, make a mark. But that one photon appears to show an interference pattern of strikes against the detector, as if the photon took multiple paths and made multiple hits on the detector. We see this interference pattern as a wave, which we would have expected to have been made with multiple photons. Moreover, when we try to measure the passage of the photon though the slit, we see only the one particle and its impact, not the wave. The observation changed the experience. Most distressing of all: nothing is determined with certainty, only by cumulative probability.
Consider what these theoretical statements suggest:
- One photon appears to demonstrate the effect of multiple photons
- The same photon can be both particle and wave
- We can control whether we see one or the other by looking at it (whatever ‘it’ is)
- A definitive answer does not exist
Things popping in and out of existence, things transforming their essence, things in all positions at once, with no hope of knowing with any certainty what will happen. Seems a bit dodgy to me.
The explanation, so far as I understand it, is that subatomic particles have the potential to become all those things, in a different form of existence. They exist as both particle and wave so long as we don’t look. Still seems a bit dodgy.
But my ‘dodgy filter’ appears to need recalibration or replacement. These extraordinary assertions have been ‘validated’ by experiment: experimental results are consistent with the theory. Nonetheless, I am uncomfortable with something so inimical to the stated principles of reasoning. And surely some of the notions are a bit fantastical, like the edicts of the Red Queen in Alice in Wonderland: “Verdict first, trial later”. For example, if you follow some of the Feynman theories, it is possible to come to absurd conclusions about an electron’s infinite mass; these conclusions then require ‘renormalization’ to make sense. ‘Renormalization’ is alleged to be a reputable procedure, but requires the subtraction of quantities defined to be infinite.
This reminds me of an emergency call and manoeuver in square dancing. Sometimes even the best of callers find themselves in a bind; people are in the wrong positions and all the squares are different, so they call something like “Air Raid” to have all couples return to where they started. Et voila! Problem solved. hat the caller does represents a resolution, relieving tensions and settling confusions. But to apply that kind of solution for the behaviour of particles, it looks like a dodge. That said, just as the square gets resolved by “Air Raid”, the renormalization dodge successfully predicts results. What is most wondrous in the theories of the quantum physicists is the extent to which the theories correctly predict the results of experiments. They might indeed bend our understanding of identity, just as they have changed our understanding of space and time.
What to Do
Should this be worrisome? Let’s consider what happens if or when the laws of thought do not apply.
My first response might almost be flippant. How can we even pose a coherent question if we do not accept the laws of thought? Let’s go back to Aristotle on identity:
if “one were to say that the word has an infinite number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning our reasoning with one another, and indeed with ourselves, has been annihilated”
In other words, you need to use the laws of thought to dispute the laws. If you deny the laws then your argument refutes itself. Pretty neat, that: “Oh, I’ve dropped it on my foot, I have.”
The second response is to pose further questions: If theories of quantum mechanics are inconsistent with our understanding of the laws of thought, we need to consider:
- whether the laws of thought are essential as a priori abstractions, existing on a more objective plane than any physical reality; we then use those abstractions to understand the observations we have made of both the Newtonian and sub-atomic worlds; or
- whether the laws of thought are only laws for the Newtonian reality in which we live, love and die – perfectly adequate for that purpose, but not necessarily explanatory, enforceable or even applicable to the other realities which modern physics and astronomy are beginning to uncover.
I would not offer a definitive answer here – certainly not to this crowd! But part of that reluctance is my belief that definitive answers do not exist. What the evolution of the physical sciences has taught me is that explanations or models of the physical world are first and foremost theories. The theories will be adjusted over time as new evidence requires – such as the observations of the behaviour of sub-atomic particles, waves or whatever they are. I don’t see why this view cannot apply to what we call the laws of thought. The basis upon which we assert the immutability of the laws of thought seems to be that these laws could not change or become non-descriptive in any circumstances whatever – certainly in the Newtonian universe, most probably in the quantum universe and possibly even in alternative universes having ten dimensions, or where the speed of light is not the same or the space-time continuum functions differently. If the laws are immutable, the laws are in fact able to explain events in all possible universes, it’s just that we haven’t seen how yet. In those circumstances, the laws of thought would have the expository power of a deity.
Somehow I’m not persuaded. Another possible explanation is that we are imposing a traditional vocabulary on events and on quanta which is not suitable to the environment – like saying “nice ship” when describing my kayak. Indeed, the uncertainty principle or the observer effect suggests that we may not have the tools or the concepts or the language to properly identify quantum phenomena. Schrödinger’s cat will forever be a conceptual entity only. Bye bye, minoo.
Another related alternative is to suggest that the laws of thought are tied directly to observable events in the Newtonian universe, but are not necessarily consistent with quantum states, alternate universes and other fantastica envisaged by modern physics. By all means try to use them, but as a ‘testable’ hypothesis. What would we be afraid of? Our Newtonian world remains the same. I think that this is where I would come out and take a “Schrödingerian” position. The laws of thoughts are theories: serviceable and enforceable in our physical world, but possibly adjustable in worlds of which we have no direct experience.
I see no good reason to assume that the classical laws of thought apply outside the universe we experience directly. To assume the laws of thought apply elsewhere in the multiverse is no more persuasive than arguing that this is the best or worst of all possible worlds.
Suppose then there are infinite laws of thought, a set for every universe in the multiverse. Would there be any unifying principle which tied all the universes together under the heading of ‘all that exists’? A deity would probably do in a pinch, but that seems to be an “Air Raid” of an explanation.
My original text for this lecture proposed to stop right there. But some of my reviewers said that I really shouldn’t leave people hanging, that I should come out with a stronger position than the creative ambiguity I have offered so far.
I small devil inside of me wants to say: “Wait for the next Installment; all will be revealed”. Those of you who have studied to works of Charles Dickens or Wilkie Collins will remember that their novels were serialized in monthly installments. People used to line up to purchase the next one. Somehow I don’t see a crowd lining up for my next installment, so I might as well spew it all out here.
To re-start, I’ll re-state an earlier conclusion: I see no case for asserting an absolute truth to the laws of thought, insofar as ‘absolute’ is construed as applicable to all possible universes. I happen to believe that the only basis upon which one can assert the applicability of the laws of thought is through observation. I hold that belief for at least three reasons.
First, we cannot use the tools of logical analysis to verify the truth of the laws of thought, as it is those very tools which require verification: we would be chasing our logical tail. I am aware of Aristotle’s insistence that without the absolute rules one cannot make sense of anything, but that’s just “Here be dragons!” scare-mongering. Lots of stuff doesn’t make sense – Donald Trump for example – but we try to deal with it.
In any case, secondly:
Nothing can be deduced
If nothing is assumed.
All that says is that you must start somewhere. So we have axioms, which we accept as true without evidence. Were we asked to justify our axiom, chances are we would refer to its necessity to make sense of the real world.
And finally, our experience – our observation – can be checked and measured and replicated. It is an experiential observation that the sun rises in the east, not an analytical one.
I have argued earlier in this talk that the laws of thought appear to apply only here in the Newtonian world – that there is credible evidence that they do not apply in the quantum world. This is the observation from experience.
But let’s not get too excited about this conclusion. If the laws of thought only apply here in the Newtonian world – in the sub atomic world or an alternate universe the laws might be different – that conclusion demands no changes at all in practical philosophy. By practical philosophy I mean philosophy that applies in the world in which we live: ethics, for example, or political philosophy. Yes the assertion makes a mess of metaphysics, but so it should. If particles can exist and not-exist simultaneously, if photons can be both wave and particle, there appear at least two examples where the laws of thought do not appear to apply. Absolute statements cannot be trusted. My assertion also causes difficulties for epistemology, as it shakes the idea of propositional knowledge. But it doesn’t shake the life out of it, as propositional knowledge can be based on ‘knowledge-how’ and still be valid as a useful abstraction.
We do like our absolutes. We have a need for an anchor.
To quote Lori Anderson:
‘Cause when love is gone, there’s always justice.
And when justice is gone, there’s always force.
And when force is gone, there’s always Mom. Hi Mom!
I am not sure whether or not I find it unsettling that other layers of our reality and other possible universes might operate under different laws. While I am confident that such a possibility will not affect my day to day life, I find it a little spooky that all around me might be different worlds with different logical rules and physical laws. Even the bizarre situations of the Time Lord Doctor Who seem to obey our laws of logic.
However, we need not abandon all sense of certainty, no matter how schizoid the behaviour of wave/particles. There is no law of though which says the sun must rise tomorrow, but rise it will and we can be certain of it. In the event it does not rise one day, then questions about certainty will be moot to say the least.