In the previous post, I gave a brief overview of the history of knowledge (otherwise known as epistemology) and argued that humanity has slowly given up essential tools to assessing reality. During the section devoted to ancient realists, I mentioned the three laws of logic as they pertained to how realists viewed the world. In this post I would like to go a little further with these laws by providing definitions as well as some practical examples of how they work.

These laws, originally presented in Aristotle’s Posterior Analytics, are as follows:[1]

The Law of Identity

Definition: A is identical to itself and different from other things.

This idea may seem too commonsensical for anyone to bother postulating it as a formal law of logic, but do not discount its simplicity. Being aware of the Law of Identity can actually save your life. Imagine waking up in the morning and stumbling into your bathroom where you open up your medicine cabinet and see two bottles of pills in tablet form. One says “Tylenol” and the other says “Arsenic”. The Law of Identity states that Tylenol is Tylenol and cannot be anything other than Tylenol. The same is true for the bottle of arsenic. So we could say, then, that a person is not justified in swallowing a couple of tablets of arsenic while pretending that it is identical to Tylenol. As an aside, the Law of Identity really becomes useful when figuring out whether the mind and the brain are identical. For my thoughts on that issue, click here.

The Law of Noncontradiction

Definition: A cannot be both true and false in the same sense at the same time.

If I were to tell you that my car was a black Camaro, it would be impossible for my car to be a black Camaro and not be a black Camaro at the same time. Pretty simple, right? This law is helpful in discussions about the nature of truth. For example, when disagreeing with others some people like to say, “What’s true for you is not true for me.” Unless the conversation is about something subjective (like favorite ice cream flavor) the Law of Noncontradiction reveals that statement to be incoherent. For example, if I were to tell you that the entire world we experience is an illusion (which is a typical Hindu belief), then the world cannot both be an illusion and not an illusion at the same time. Likewise, if I were to tell you that there is no such thing as a supernatural aspect to reality (which is a typical materialist/Atheistic belief), then my statement could not be true on Wednesday and false on Sunday. It is either all true or all false.

The Law of Excluded Middle

Definition: A is either true or false.

This idea seems to be a repeat of the Law of Noncontradiction. But, while the two laws entail each other, they are not the same. Remember, the Law of Noncontradiction states that an idea cannot be both true and false at the same time. Well, the Law of Excluded Middle simply states that there is no third option for an idea being true or false. So, for example, if I had a belief that the tablets I just swallowed were Tylenol, then it is only either true or false that the tablets are actually Tylenol. There is no third option between true and false.

Practical Application

How does this apply to, well, everything we do? Take your experiences driving a car as an example. How do you know that the car keys in your pocket belong to your car? The Law of Identity. Your car keys cannot be identical to any other set of keys except itself. So you get in your car and drive on the street. Why should you not drive on the left side of the road (in America)? The Law of Noncontradiction and Excluded Middle. If you decide to drive on the left side of the road, cars will quickly speed towards you. It would be impossible for these cars to be speeding towards you and not speeding towards you at the same time. It is also impossible for there to be any other option than the cars’ either speeding towards you or not speeding towards you. If, somehow, you were brave enough to disregard the laws of logic, what do you think would happen next?

Reality. Would. Seriously. Harm. You.

This is only one of many examples of how we use the three laws of logic regularly (whether we are aware of it or not). They are so embedded into every aspect of our existence that, if these laws somehow went away, reality would be nothing more than incoherence and randomness. Therefore, beware the worldviews that can neither give a proper accounting for these laws nor affirm their value/necessity.


[1] I have used updated language consistent with Aristotle’s definition in Posterior Analytics.

1 COMMENT

  1. Good day! I could have sworn I’ve been to your blog before but after looking at a few of the articles
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  2. Well, being picky, you might have dreamed that you took the tablets, in which case there is a third option.

    The LEM only applies to a true contradiction. A true contradiction is A/B where one of A or B is false and one is true. If this condition does not hold, (as when you dreamed the tablets) the LNC would not apply. Thus we have to know that one of A or B is false and one is true before we can know whether it would be legitimate to apply the LEM.

    I mention this because if we forget it then we may see a contradiction in Buddhist doctrine where there isn’t one, as perhaps you do in your post of the Buddhist view of self. The study of the dialectic is a central part of the curriculum for the Buddhist universities, partly since self-contradictions are such a useful way of eliminating false ideas.

    As all distinctions would be emergent, it would be impossible for Buddhist doctrine to give rise to a contradiction.

    • Hello again,

      And thanks again for the comment! Your suggestion sounds an awful lot like its trading on an epistemological definition of truth rather than an ontological one. As a metaphysical realist (if you hadn’t already guessed), I would simply say that LNC and LEM hold given my view of truth. At this point, I suppose we’ll rest on the particular axioms that we believe have the best explanatory power.

      With regard to your comment about distinctions in Buddhism as emergent phenomena, I would point back to my comments and questions in response to yours at the bottom of Problems with the Buddhist View of the Self.

  3. No, I’m not holding to any particular idea of truth. I’m just restating the rules as laid down by Aristotle. In order for the ‘laws of thought’ to work we have to be sure that A and non-A are a true contradiction such that one is true and one false. If we do not know this then we do not know whether the LNC or LEM can be legitimately applied. I was questioning whether your pill-taking example met this criterion. If not, then it would be a category-error.

    I would propose that the avoidance of this kind of category-error is the whole secret of metaphysics. We often forget the small print for Aristotle’s method, and when we do we see a mess of dilemmas that aren’t really there. .

    • Just so I’m clear, are you referring to Aristotle’s ambiguous qualification for LEM with regard to future contingents? Because, if so, I find the Thomistic solution (that is, placing the indeterminacy of a true contradiction on the viewer, not in the world) to be sufficient. This is why I referred to Bertrand Russell’s distinction between an epistemological and ontological view of truth. If epistemological then it is acceptable to say that LEM doesn’t always hold. If ontological then it is acceptable to say that a proposition can be true or false even if we don’t know it is — in which case LEM still holds.

      Is this what you were getting at, guymax? If not, I apologize for misreading you. Please bear with me as I’m right in the middle of term papers and finals.

  4. I think I see your point. But I see no need to distinguish between ontology and epistemology here. Nor would it be a question of what we know or don’t know.

    As long as we define the answers to a question so that one of them must be true and one false then the laws will work well. Suppose we ask, Did John score a goal against Arsenal last week? We may not know the truth, but we know that the answer will be yes or no, and so we can apply the laws. If we ask, Is John English or Welsh? then to apply the laws would be a mistake, since he might be Scottish. Our question makes an assumption that renders it illegitimate as a dialectic question.

    And so in metaphysics we have to be very careful. Suppose we ask ‘Did the universe begin with Something or Nothing? We are assuming that there is no other answer. But this would not follow analytically or tautologically from the question. We cannot know that it must be one or the other unless we define our terms so that there could be no other answer. This is not easy to do. If we fail to do this then we cannot be sure that the LEM of LNC applies.

    So we wouldn’t have to know the truth to use the laws legitimately, we would just have to choose our questions very carefully. In ordinary life this is not too great a problem. If we ask whether the weather is sunny or wet then this is a mistake since it could be neither or both, but we know what we mean and can get away with this kind of sloppiness. In metaphysics, however, such sloppiness is a very big problem and causes much confusion. It causes confusion in QM also, where we might naturally want to assume that an electron is a particle or a wave but cannot because it could be neither or both. So QM leads to no violation of the laws even though it might appear to produce a contradiction due to our inability to imagine something that is not unambiguously either a wave or a particle.

    The crucial point is, and Aristotle makes it at length, we cannot depend on his laws of thought unless we can be certain that our dialectic questions must, by definition, have only two answers, only one of which is true.

    This is a simple point but it is very often forgotten, even by well-known philosophers. When we forget it our reasoning process goes horribly wrong, and metaphysics becomes a mess of unnecessary dilemmas.

    Thus when the LEM states that A must be true or false this is not a rule for answers, it is a rule for questions. If the question does not obey it then the rules will not work.

    Does that make sense? If you’re interested, then for a full discussion of this issue I’d recommend Whittaker C.W.A., ‘Aristotle’s De Interpretatione: Contradiction and Dialectic’. (It is in ‘De Interpretatione’ that Aristotle explains the use of his dialectic method).

    • Yes, it does. And this is an excellent point to make, guymax. Very well said.

      I think this is what I meant by falling back on our particular axioms. As I had mentioned, I’m operating under the presupposition that there is a particular quality about the weather (to use your analogy) that is ontologically true whether we’re sloppy about our semantics or not. I think this applies to QM, or at least to what QM can tell us about reality. Our view is still so hazy at this point that I think Feynman’s comment about no one understanding QM is still very relevant. At least, no one knows which interpretation of QM is correct. I tend towards Einstein’s attitude in that I believe that the indeterminacy so far experienced in QM is due to our epistemic limitations and not necessarily an ontological indeterminacy. But I acknowledge that this is my own presupposition I’m bringing to the table as a starting point out of the realist structure of my worldview. Which means I could be wrong about that.

      Thanks for the suggestion. I’ll check him out too. As my wife can tell you, I read everything people recommend to me. So I’m glad for the suggestions! Thank you.

  5. Hope you like it. It came as revelation to me. I was already convinced by the Buddhist view when I read it, but could never quite see how to reconcile this view with the ordinary logic of metaphysics. It was getting into the details of Aristotle’s rules that solved the problem. He saw all the pitfalls and allowed for them.

  6. […] All religions are true. This cannot be the case since all religions possess exclusive qualities that negate other religions’ truth claims. For example, Muslims believe that Jesus is not divine but just a man (like Muhammad). Christians believe that Jesus is God. Both propositions about Jesus cannot be true at the same time (law of noncontradiction). […]

    • Thanks Jerome! Glad this post could help. You know, Jerome, we have to be mature in our thinking (1 Corinthians 14:20) so that we can destroy speculations and every lofty thing raised up against the knowledge of God (2 Corinthians 10:5). Ordering our thinking with regard to logic and philosophy helps us to see through many lofty things, my friend! May we always be prepared and ready (1 Peter 3:15), sir! 🙂