Browse Our Articles & Podcasts

No Third Way: The Fundamentals of Rationality


It did seem as though many of the Synod fathers were proposing something that is logically impossible. It was not said out loud, but the implication was that they were asking, “Between yes and no, being and not being, sin and not sin, death and life, can we have a ‘third’ option? And if so, is this where ‘mercy’ lies?”

One of the reasons everything that went on at the 2014 session of the Synod on Marriage and Family has been so uncritically welcomed in the secular world and in the Church is that people are not taught any more the fundamental concepts of rationality. And the idea of a warm, cuddly, non-judgmental and “merciful” “third way” between condemning sin and total permissiveness, is certainly very appealing to people who have no notion of what the jiggety they’re talking about.

Or, as our friend Patrick Archbold said, “The idea that there is some middle way between God’s law and God’s mercy is merely a sop to the weak minded and the weak willed to make them feel better about accepting a little heresy.”

But I think so little about how to think is taught to most people, and so much has the corruption of the intellectual life seeped into the public discourse, that we might be being a little unfair. People are not taught that a thing and its opposite cannot both be true. They are not taught that there can’t be anything between two opposed propositions. And they are not taught that a thing is what it is and is not another thing.

But it’s not really that hard to understand the foundations of rational thought, and from there, to extrapolate a method (logic) of figuring out what is and is not true, once they’re adequately explained. These laws are so basic that they are like the understructure of a house, and if you try to ignore them, it’s like trying to build a house in mid-air. This is why we call it “metaphysics,” because it’s the stuff that underlies our understanding, it’s the conceptual framework we use to hang thought on.

Aristotle codified these laws, but they are named and discussed in the ancient literature all the way back as far as anyone has recorded. Wikipedia (with a certain amount of deafness to the irony) describes them thus: “The laws of thought are fundamental axiomatic rules upon which rational discourse itself is often considered to be based.”

Without these three basic “axiomatic rules,” it is impossible to conduct any kind of human intellectual work. They are to the ability to reason, (which means to figure out what is and is not true) as basic arithmetic is to particle physics. Indeed, we would never have figured out anything about basic arithmetic if we didn’t start with these fundamental laws, even if only unconsciously.

They are closely related and sound quite a bit like each other, and when you say them out loud, you wonder why anyone would have bothered to say such obvious things: The Law of Identity, the Law of Non-contradiction and the Law of the Excluded Middle. 

I’ve written a lot in the last 15 years about the Law of Non-Contradiction, which gets expressed in a lot of different ways, but simply says that “a thing and its opposite cannot both be true in the same sense at the same time.” I can’t be both in the room and not in the room at the same time.

From this we get notion that some things can be “mutually exclusive,” or “logically incoherent,” which can be applied to a lot of things in life. And we can say from this idea that some statements are meaningless or nonsensical because they are self-contradictory: “My brother is an only child.” You can’t be a polytheistic Muslim, for instance, since the one basic tenet of Islam is that there is only one god.

(Interestingly, the LP of Non-C is also where we get irony. If irony is simply a literary or rhetorical device in which a statement is made that is clearly opposed to the facts – “Oh, what a LOVely day!” when it is pouring with rain – it would be impossible if we didn’t have the basic concept of identity and opposition, that there can be a thing that is utterly and completely, perfectly and irreversibly not another thing. Which, I think, is why the people we often call “liberals” are often profoundly “irony-impaired”. Liberalism can only be achieved in the human mind by a corrosion of intellectual powers brought about by the attempt to deny or ignore one or more of the Three Laws of Rational Thought.)

When we say that something is self-contradictory or logically contradictory or logically incoherent, we are really saying that the given statement is meaningless. As Douglas Adams once facetiously put it, it “disappears in a puff of logic”.

So important is it, and so utterly impossible would it be to proceed without it in any intellectual endeavour, even one as simple as a conversation about the weather, that the Persian philosopher, Avicenna once famously wrote, “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.” And he recommended this ferocious treatment because in a very real sense, a person who tries to deny the LP of Non-C cannot be spoken to reasonably at all.


One of the things that has made me very, very worried about the world is the fact that this basic law of rationality is now routinely denied (yes, that’s ironic… I see you’re catching on). I can’t tell you how many times I’ve had people say to me, with perfectly straight faces and utter sincerity, “But there’s no such thing as objective truth…” The very, very popular notion that “my reality is different from your reality” or “you make your own reality” or “everyone decides for himself what is and is not true” are all implicit denials of this first, fundamental law of rational thought, without which we have no tools to even describe reality. These are all statements that are completely devoid of meaning at a most basic logical level. But they are parroted again and again by nearly everyone you meet and almost never refuted.

A lot of people out there in the world couldn’t understand why so many Traditionalists were so upset when Pope Francis said in that La Repubblica interview, “Each of us has a vision of good and of evil. We have to encourage people to move towards what they think is Good.” (In the end, it turned out that the interviewer may very well have simply made the comment up out of his own head, so… whatever. But even if Pope Francis didn’t say it and Scalfari made it up, it shows how far down we have sunk that this “leading Italian intellectual” thought it was something profound and meaningful enough for a pope to say. This is the sort of thing that “leading intellectuals” think makes sense.)

I could go on.

But the next thing that we have not talked about much is these other two: the Law of Identity and the Law of the Excluded Middle.

Again, simply, they are, respectively, “A thing is that thing and not some other thing,” and “Between two opposed things, there cannot be a third, middle thing.”

The Law of Identity is sometimes put like this: “For any proposition A: A = A” or like this, “each thing is the same with itself and different from another” – but you get the idea. Now, to get an idea of how fundamental this is, try for a moment to imagine a universe where this idea is not. Imagine this proposition: “A thing is the same with another thing and not with itself.”

Read it again a few times until it sinks in. It’s not possible. It is “anti-Real”.

And you can start to see how these metaphysical concepts are the notions that underlie all our other ideas about the nature of reality. Euclid used them implicitly when he invented geometry, which is really just the first stages of mapping reality in mathematical terms. (OK, yes, I know Euclid didn’t “invent” geometry… but you get my drift.) In fact, it could be argued that the Law of Identity is that notion from which all mathematics starts.

Euclid said in Book 1 that the very first of his “Common Notions, sometimes called axioms,” that are the first starting point of all the rest of his mathematics, is “1. Things which equal the same thing also equal one another,” … and he was off!

And the Law of the Excluded Middle that Aristotle described as, “there cannot be an intermediate between contradictories.” Think about it. What is there “between” being in the room and not in the room?

Aristotle wrote: “there cannot be an intermediate between contradictories…This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false.”

Reminds you of anything? “Woe to those who call evil good, and good evil; Who substitute darkness for light and light for darkness; Who substitute bitter for sweet and sweet for bitter! Woe to those who are wise in their own eyes And clever in their own sight!” (Isaiah 5:20-21)

And “I call heaven and earth to witness against you today, that I have set before you life and death, the blessing and the curse. So choose life in order that you may live, you and your descendants, by loving the LORD your God, by obeying His voice, and by holding fast to Him…” (Deuteronomy 30:19-20)

Note that there isn’t anything in there that says, “Unless you find it very difficult to decide, in which case, you can have a third thing that is comfortable and non-threatening.”

Now, I realise that even with this little brief introduction it is clear that we could go on all day. And all night. And for the next century, and people have. But this is where you start, and without this, no start can be made. And attempting to make a start by starting without any of this stuff, you go nowhere.

So, when a bishop or a pope says to you, “There should be a third way of ‘mercy’ between yes you can and no you can’t,” tell them Aristotle disagrees.



Originally published on October 20, 2014.

32 thoughts on “No Third Way: The Fundamentals of Rationality”

  1. Great essay.

    I once had a brief discussion with a liberal-minded college student who argued that the main problem with conventional (read: conservative) thinking is that it tended toward the binary. For instance, the insistence on two options, A or B, with no middle ground or room for ambiguity.

    As a mathematician, I naturally responded that of course there might be other options besides A or B — However, there are no other options when you formulate the choice as A or not-A. If you want to say that B is not the same as not-A, that is fine. Go ahead and make your case. However, if someone is explicitly saying you must choose between A and not-A, it makes no sense whatsoever to accuse them of a lack of nuance or subtlety or to accuse them of fallacious “binary” thinking.

    Now I know I was explaining the law of excluded middle. Too bad I didn’t know that I was explaining Aristotle at the time, because that would have lent itself to some pithy rhetoric. (On the other hand, maybe the point was better made without an appeal to authority.

  2. In so many discussions online and in person, I try to coax out early whether or not a person believes in the principal of non-contradiction. If they don’t abide by this principal, I end the conversation avoid any communication in the future with them, because there can be no discourse. If someone believes that A can equal not A, you can’t discuss anything meaningfully. If you can’t discuss anything meaningfully, there’s no point in even opening your mouth.

    This sort of thing doesn’t work quite as well with relatives, but I can force myself talk about the purely superficial with them. It’s taxing, but they’re family.

  3. It is usually at this point in a conversation that the liberal “Catholic Answers” listener attempts to use, “But the Catholic Church is about both/and, not either/or.” And then I silently scream inside my head.

  4. Thank you, Hilary White for a great article. Sheepishly, I did not formally know of these laws, but thanks be to God I do possess them in my thinking and can now understand more fully understand the complete disconnect that is going on. Aaron Traas, I like your approach and think I will employ it.

    • Yes, that’s normal, there’s no need to feel sheepish for not knowing that it’s all been worked out and given names. There have been smart people around thinking about this stuff since Aristotle invented being smart. People are mostly capable of rational thought, which means that they implicitly accept the Three Laws. But it’s worth looking at more deeply. When I discovered all this stuff had been written down and worked out, I found a whole new world of clarity of thought opening up the more I read and thought about the implications. If you read it and start to comprehend it, you find your own ability to think clearly and reason accurately and quickly increases. It’s like it makes you smarter. And it will help you understand religion too. I remember the great moment when I realised that geometry was a map of the very nature of reality, and the existence of these perfect mathematical realities was a secret finger pointing to the existence of a rational God. I was 22 and taking a math upgrading course for adults, and I became so excited I started babbling to my teacher about Platonic forms, who had no idea at all what I was going on about, poor chap.

      • Thank you! I will certainly “take a peek.” It seems a bit daunting, but essential, particularly when obfuscation of Truth and Reason is running amuck.

  5. Thanks for the refresher Hilary. Any suggestions on where to start for those of us who missed out on Aristotle growing up? I’ve always been a fan of Mortimer Adler but any other suggestions for teaching yourself logic would be appreciated.

  6. It is important to understand the fundamentals of logic and rational thought. It is equally important to understand the proper application, and limitations, of logical thought in rational discourse. It is quite possible to formulate a perfectly logical argument that is completely and utterly wrong if it is based upon false premises. I would like to suggest that some of the reaction to the reports surrounding the synod is premature and emotional.

    The questions the Synod wrestled with were not simple binary formulations. There is not a question of should the Church preach doctrine or mercy? The two are indivisible. The truth that the Church preaches IS mercy! Rather the central question that should be asked is how does the Church preach the truth of it’s doctrine in a way that the mercy within is revealed to the sinner as salvation rather than condemnation?

    There are many issues related to the Church and family life. With regard to marriage the questions appear well known. Homosexual marriage or not? Divorce and remarriage or not? Fornication and/or cohabitation or not? Contraception or not. These seem obvious and binary but they are not. Others are There are some that are not so obvious. In the zeal to “minister compassionately” to divorced and remarried Catholics many parishes have overlooked those whose spouses have left the marriage and remarried but whom wish to remain faithful to their marriage vows. Each of the marriage question above contains elements of doctrine (homosexual conduct, adultery, fornication, and contraception are all contrary to he doctrine of the Church and therefore things which take one away from the mercy of Christ) but also elements of pastoral care that are multi-faceted. How does one explain to the homosexual that his attraction (which he might view as given to hi by God) is a temptation that leads to death while still showing respect for him as a child of God who is due the same dignity as any other fallen child? How does one do so in a manner which does not seem to endorse the sin?

    It seems to me that there is a spirit of division in the Church, and society, where we are quick to defend our position and slower to seek the will of God. We seek to criticize rather than understand. We label rather than relate. The “conservative” bishops might be the pure defenders of the faith while the”liberal” bishops are heretics undermining the Church. The “liberal” bishops might be attempting to show true pastoral care while the “conservative” bishops are rigid and unmerciful. Likely these caricatures apply to some on either side. It is also possible that questions are complex and the challenges difficult and there is value and truth to be discovered on both “sides.” Those with a different point of view might not be evil – they just might hold tighter to a different portion of the truth than I do.

      • I do not understand your response. Do you intend to demonstrate the irrationality of Patrick Archbold’s statement, quoted here approvingly, in your discussion of syllogisms and the fundamentals of rational thought?

        It is irrational to consider, as you and Patrick apparently do, whether pondering if there is a middle way between God’s Law and God’s Mercy is simply a means to find comfort in heresy. It is irrational because God’s Law and God’s Mercy are the same thing! To discuss whether there is a place between the two is to misunderstand both.

        In the context of the synod, which is how you introduced this article, the discussion of the law of the excluded middle is completely misapplied. The Synod was not wrestling with issues that devolve into binary choices. They were not struggling with the identity of a thing. The Synod was wrestling with complex questions of multi-level optimization. What is the most effective way, in this time, and this culture stew, to show people that God’s law is both loving and merciful? How do you welcome sinner’s enough so that they will come and hear and recognize their sin and accept the grace of repentance and forgiveness.

        It is necessary to apply the laws of rationality to these discussions. It is equally important to have a spirit of charity when doing so. It is quite one thing to use the laws of rationality to demonstrate the weaknesses in another’s proposed approach, or the strength of your own. It is quite another to misapply those laws and level charges of accommodation of heresy against those whose irrationality is, apparently, no worse than your own.

        I think your article would have been far more valuable if it had not been tainted with an inappropriate connection to the events of the Synod.

          • Technically you are correct. One must distinguish between the moral law and the OT law of works. One must also distinguish between love and mercy. In the context of this discussion though, these distinctions are pedantic.

          • It is hardly pedantic. To suggest that love and mercy are the same thing or that truth and mercy is the same thing or that the law and mercy is the same thing is to do exactly what an irrational, unthinking person does. In layman’s terms it is a leap of logic. It waters down the deeper meaning of these concepts and promote false ideas about them, which possibly could have eternal consequences.

  7. Hilary, and those of you who have the time, the very wise thomistic philosopher, Duane Berquist, gave a series of philosophy/theology lectures for beginners at a monastery in MA, and the monks informally recorded the talks. You may enjoy them. I have hard copies that they gave me for my own edification, but someone else put them serially online (although the talks on Aristotle’s De Anima appear to be missing and perhaps others). They are eminently worth hearing even if only to witness a wise man.

    Intro & Logic
    Philosophy of Nature
    Love and Friendship

    Theology 1: On the nature of sacred doctrine
    Theology 2: On God
    Theology 3: On the Trinity

  8. A few observations:

    1) When you point out the law of non-contradiction, they’ll simply use this clever trick: “When you get a contradiction, make a distinction.” And so the distinction between pastoral and doctrinal is born, because it is harder to make the case that a given pastoral action is contrary to a given proposition and therefore inconsistent with it.

    2) Something tells me our German friends in the episcopate have been reading Hegel (and his descendants), whose whole programme seems to be about overcoming Aristotelean metaphysics and Historicising it, meaning: lending each system of metaphysics of a given era a best before date.

  9. Have I told you how much I love 1Peter5 lately! Thank you. I really loved this article and it helps to make sense of nonsense that is everywhere! Thanks for clearing everything up!

  10. Thanks Hilary. Excellent. Surprised at low level of awareness. This was basic stuff at Jesuit Universities in the 1950’s.

    Might we consider the folks who disagree with these propositions benighted, lazy, crazy, or deprived due to their Liberal education. And, of course, we will show mercy by praying for them rather than arguing.

    Someday if would be nice if you could get around to discussing the 24 Thomistic Theses.

  11. The Church has practiced ‘contradiction’ for centuries. It says marriage is indissoluable and then grants annulments. The pretzle logic required to defend annulments and the scandel produced by the circumstances around many annulments make it clear that in reagards to marriage the Church has already taken a ‘third way’.

    The Synod on the Family are just the fruits of a harvest that has been centuries in the making.

    • Except that Christ Himself noted exceptions to His stated law of indissolubility. And, also, He gave Peter and the Apostles the sweeping plenary power to bind and loose.


Leave a Comment

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Popular on OnePeterFive

Share to...