I just stumbled on this argument from a Christian website that claims it is from C.S. Lewis' Mere Christianity:

The moment you say that one set of moral ideas can be better than another, you are, in fact, measuring them both by a standard, saying that one of them conforms to that standard more nearly than the other. But the standard that measures two things is something different from either. You are, in fact, comparing them both with some Real Morality, admitting that there is such a thing as a real Right, independent of what people think, and that some people's ideas get nearer to that real Right than others. Or put it this way. If your moral ideas can be truer, and those of the Nazis less true, there must be something-some Real Morality-for them to be true about.

I think this is an interesting argument, and even an interesting form of argument, even if the conclusion is unsound. For instance, if you say that one person is taller than another, then it seems logically necessary to infer that there must be something like distance for two heights to be comparable in this way. But I don't know of anything in formal logic that allows for such an inference. Is this logical inference valid?

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    Doesn't this ignore the fact that moral systems can be self-referential and that they often come packaged with the premise "this moral system is better than all others", as well as criteria for preferring one moral system over another, usually according to how well each of the other systems agrees with the original system. – Tim kinsella May 9 '15 at 0:41
  • I recommend reading Book I of Mere Christianity (it appears to be public domain and many PDFs are freely available), which is a fairly short 5 chapters and covers this topic. His argument has additional context and certainly is broader than just this, though I don't think that impacts your question of the validity of this argument overall. Certainly he addresses this particular argument (that people at least act as though an absolute morality exists, regardless of what they profess) a few more times from a couple different angles or at least with some different examples. – LightCC Jul 24 '17 at 18:21

I think Lewis's main argument is relatively clear. It's just a modus ponens:

  1. If it is a fact that moral code M1 is better than moral code M2, then there must be some absolute standard A in the light of which M1 is judged better.
  2. It is a fact that moral code M1 is better than moral code M2.
  3. Therefore, there must be some absolute standard A in the light of which M1 is judged better.

(1)-(3) is clearly a valid modus ponens argument, so if the premises (1) and (2) are true, (3) has got to be true too. The more interesting question, as usual, is why we should believe (1) or (2) true.

It is hard to deny (2). It's hard to imagine somebody giving us a plausible reason to think there are no instances of one moral code being superior to another. (It might be hard to tell which of two codes is superior. For instance, M1 might be superior to M2 in one respect, but worse in another. But that won't detract from Lewis's point.)

(1) is the odder looking claim to me. Burning paper is hot; molten lead is hotter, but I can't see why that would imply that there is some absolute standard of hotness. (1) looks like a more plausible claim about a property like grey. If one thing is bluer than another, it looks more likely that there has to be some canonical instance of grey. Still though. I'm not sure that's even right. Suppose we have a spectrum of fifty shades of grey. The ones at the edges will look "whiter" or "blacker" but that might not mean that there are a couple of different shades in the middle none of which is definitively grayer than any other.

So my vote is that Lewis's argument here is valid, but of questionable soundness, because (1) is false, or at least in need of serious qualification and defense.

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    My sense is that (1) isn't a premise in his argument, but itself a logical inference. But because he didn't symbolize his argument, it's hard to tell what his intention was. Reading it, my sense is that we are supposed to read a logically necessary inference from judging one morality better than another, to the establishment of a basis for judging moralities as better or worse than one another. In your example, wouldn't temperature suffice as an absolute standard of hotness? – Kevin Holmes Jul 20 '14 at 0:05
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    (1) pretty much has to be a premise, because he's taking it as obvious that some systems are better than other, and therefore concluding the existence of an absolute standard. The only way to make an argument like that valid is with an if . . . then premise. And it isn't "temperature" that is the relevant thing here. Lewis's idea isn't just that two things can be compared according to some scale--but that they can be judged by how well they conform with some perfect standard. But temperature is a scale, not a perfect standard. – shane Jul 20 '14 at 0:48
  • Incidentally Aquinas does use temperature as an example in a similar argument, but his reason for doing this is that he actually believes that fire is literally the hottest thing there can be. This is just part of the aristotelian natural philosophy according to which everything consists of earth, air, fire and water. Fire has the property of heat essentially, and anything else is hot insofar as it's got some fire in it. Hence fire on its own is maximally hot. – shane Jul 20 '14 at 0:50
  • But WHY does the judging of some systems as better than others imply an absolute standard? This sounds logically necessary to me, yet it doesn't seem to belong to the existing canon of logic. – Kevin Holmes Jul 20 '14 at 8:41
  • I don't think Lewis means it to be a trivial truth of logic, but some substantive fact about what it means for one thing to be better than another. At any rate, I'm not sure the principle's true, let alone logically necessary. – shane Jul 20 '14 at 11:39

The argument is sound, minus a vacuous error:

  1. Premise: A > B
  2. Assume: '>' ∈ { A, B }
  3. Then: A is the standard by which B is measured

The following would appear to be an instance of #2:

For the LORD is a great God, and a great King above all gods. (Ps 95:3)

     God =        אֵל = 'el
     gods = אֱלֹהִים = 'elohiym

However, it is not clear that this damages Lewis' overall argument. For consider that #2 essentially assumes that A = God. It is typically said that God is the standard of what is right and what is wrong; this means he can be compared to that standard, by being identical with the standard. He is, by definition, greater than anyone else, better than everyone else, etc. I detect no contradiction.

Is it the case that #2 immediately sets A = God? I claim that the answer is yes, although if A is finite, we should perhaps say A = god. But we are used to there being many different gods, none of whom allow another to be the standard of good and evil: see the Greek pantheon, for example. It seems to me that Lewis would be on board with asserting the following dichotomy:

     I. Either you are claiming that you are a god,
    II. Or you are claiming there is ≥ 1 god who is not you.

It seems fair to say that Lewis would dismiss I. as vacuously false: who would say that? Well, Nietzsche might (I'm not an expert), but surely not the audience to whom Mere Christianity is addressed. Therefore, we are justified in rejecting #2, which lands us at:

But the standard that measures two things is something different from either.

Unfortunately, Lewis does not admit the possibility of > 1 god. I've been playing a bit fast and loose with the term 'god'; I could say instead that there could be > 1 standard of morality, such that all standards are incomparable to each other. But wait a second. Lewis is assuming that #1 is a valid operation. That prohibits any two standards from being incomparable. This allows us to construct a total order:

     i.  S1S2S3 ≤ ... ≤ SN

Here, SN is the standard by which all other Si are measured. SN is the אֵל above all אֱלֹהִים.

  • Why would more than one "best standard of morality" be a problem? Wouldn't that just mean that all the things these standards can't agree on (e.g. whether to drive on the left or the right side of the road) are merely conventional? – nikie Jul 19 '14 at 9:47
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    "Which side of the road" is not a moral issue. The problem is that the very use of the word 'best' implies comparability, which implies a single 'best'. Without comparability, you cannot know if your morality is 'best'. – labreuer Jul 19 '14 at 14:28
  • That's just my point: If there is a set of moral standards that all equally "good", but better than all others, then all the differences between these standards aren't moral issues. Society can choose one or the other based on taste or fashion or convention, because morally, they're equal. That's not a problem. (You seem to be thinking about proofs of god's existence, which is really something quite different.) – nikie Jul 19 '14 at 15:13
  • @nikie, If they are all "equally "good"", then replace '≤' with '=' at the end of my comment, point i. What you might have just done is allowed Nazi Germany to be "equally "good"" compared to every society, today. Note that I was reacting to your assertion of there being more than one "best standard of morality"; if you just meant that we can switch '≤' → '=', then okay. But if you do this, then you seem to be asserting a common standard to which all societies can be compared, with the rest just being 'taste'. Lewis would be in full agreement with such a proposition. – labreuer Jul 19 '14 at 16:04
  • The phrase was can be not always can be, so you don't get a total order. Without a total order, there is no guarantee that there is a supremum. – Rex Kerr Jul 19 '14 at 23:03

For instance, if you say that one person is taller than another, then it seems logically necessary to infer that there must be something like distance for two heights to be comparable in this way.

No, I don't think it is necessary: For that, you also need to assume some logical properties of the relation "taller". At the very least, it has to be antisymmetric (if Paul is taller than John, then John can't also be taller than Paul), and it has to be transitive (if Alice is taller than Bob, and Bob is taller than Charles, then Alice is taller than Charles). Otherwise, you don't even have a partial ordering, and it doesn't make much sense to talk about a "common measure".

Now it's probably harmless to assume antisymmetry. But I don't see how transitivity of "moral superiority" would be obvious. It could be that Alice's moral standards are "better" than Bob's, Bob's are better than Charles', but Charles' standards are nevertheless better than Alice's. Weird, but not a contradiction.

Also: Although "taller" is a property that induces a total ordering, the resulting property "length" is not independent of the observer. As the theory of relativity tells us, it depends on the frame of reference of the observer.

So, I think CS Lewis has a point that as soon as you think "my moral system is better than the Nazi's", you can't be a moral relativist any more. But I don't think you can infer a common, subject-independent measure of morality from that.

  • "As the theory of relativity tells us, it depends on the frame of reference of the observer."—ahh, but the theory of [special] relativity also includes Lorentz transforms so that you can map from one frame of reference to the next. Do you claim that morality has something analogous to Lorentz transforms? This would seem to damage your argument, for it restores comparability. – labreuer Jul 19 '14 at 16:07
  • The logical properties of the "taller" relation are known because the proposition is assumed to be understood. I also believe that the argument is unsound...mainly because while I think the argument implies a standard, it doesn't have to be an absolute standard. It could be a convention, which may imply another convention to compare conventions, and so on into an infinite regress. But I'm intrigued by this inference from the relation to the standard that defines all such relations. Is this an example of hypostatic abstraction? Still...it doesn't seem to be a standard part of formal logic. – Kevin Holmes Jul 19 '14 at 19:12

It's true-ish but overstated.

Let's suppose A and B are moral systems; we'll treat them as relations such that if M is a moral system then x M y is true if and only if x is more moral than y.

Now if you're going to say that A is better than B, then you'd better have some relation R such that A R B is true. You simply can't get around that, and that's the core of Lewis' argument.

The inference that there is a real morality M is incorrect, however. Here are two counterexamples.

Counterexample by agreement


A A B = true
A B B = true

Then A and B agree that A is actually the better moral system. This doesn't say anything about a third moral system C, but aside from the problem of B being self-refuting it's odd not to say that A is better than B here. If that's not enough, let Q be your entire set of moral systems, and then suppose that

for all P in Q
A P B = true

Then you really ought to say that A is better than B. But it does not follow that

there exists S in Q such that
for all K in Q where K != S
for all P in Q
S P K = true

which is the statement that there's a best and universally-agreed-upon system of morality.

Counterexample by example

It intuitively seems that moral systems must return certain answers, e.g.

"torturing babies" M "taking care of babies = true

is not what a moral system M should tell us. Even if we can't generate a perfect moral system, we still could generate some examples that have to go a certain way. Let's number them 1 through n; then we can score our moral systems by

count[i]{ x(i) M y(i) = true }

(Some rules might be more important than others, so we could assign a weight w(i) to getting a certain answer right if we wanted.)

A faulty system of morality would have this count (let's call it c_M for short) rather lower than n, while a moral system that is as good as we can measure would have a score of n.

Now we have a relation R that can be used to compare moral systems:

A R B = c_A > c_B

But R is not itself a moral system because we can't ask it questions about anything other than our set of examples.

So it might be true that c_LiberalDemocraticMorality > c_NaziMorality but that doesn't say anything about whether a Real Morality can even exist. For instance, it could be provably the case that certain answers are actually logically inconsistent with each other, which would make a score of n impossible.

That this means our questions are flawed, or that the trial-questions approach is incorrect is not at all obvious.


It is not logically correct that if A is better than B by some measure that there is a perfect P against which both A and B are measured. In particular, one can construct self-agreeing systems or scores on sets of examples where it is possible to say that some system of morality A is better than some other B without assuming a real morality M.

  • Enlightening! Perhaps I was expecting this sort of inference to be more involved than just seeing his use of "standard" having the form of a logical relation, but it seems to work. And I can't help but agree. Lewis says that the standard that measures two things can't be either of those things, but you give counterexamples. I can think of how this is true, to use a simplistic example, I can determine that the meter is longer than a foot, by using meters or feet, and I don't need a third standard that measures in something other than meters or feet. Thanks for your response. – Kevin Holmes Jul 20 '14 at 0:22
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    But I can't help but wonder, using my example, what if what Lewis is talking about isn't so much that meters and feet can be measured in meters or feet, but that one object can be judged longer than another only by means of a measurement such as distance. So you measure two physical objects to be longer than the other, but neither object can be the standard that you are measuring by. Even a ruler is meaningless (just a physical object) without a concept such as distance to give meaning to the relation "longer than". – Kevin Holmes Jul 20 '14 at 0:26
  • @KevinHolmes - That's why I said it was true-ish. Calling it a Real Morality is misleading, since I came up with two examples where there is no canonical or ideal morality that you compare to. – Rex Kerr Jul 20 '14 at 3:46
  • (1) R contains count[i]{ x(i) M y(i) = true }, making it a moral system, for the examples are such that they are enough to always compare any two moral systems. So R is, de facto, a moral system. (2) You really rushed through the "certain answers [...] logically inconsistent with each other", and yet it seems your argument is predicated upon it, if it is not also predicated upon (1). Would you elaborate? (3) Are you undermining a very premise of Lewis' argument, that there is a '>' operator? – labreuer Jul 20 '14 at 5:36
  • @labreuer - A single example is enough to say one moral system is better than another in the framework above. I'm not quite sure a single example of an answer counts as a moral system itself? Also, I don't have any particular set of inconsistencies in mind, but very reasonable-sounding things can in fact be inconsistent, e.g. in voting, Arrow's Theorem: en.wikipedia.org/wiki/Arrow%27s_theorem – Rex Kerr Jul 20 '14 at 22:13

The moment you say that one set of moral ideas can be better than another, you are, in fact, measuring them both by a standard, saying that one of them conforms to that standard more nearly than the other.

I think this is the most debatable step. Certainly, in moral relativism, one does not admit a single standard. If a moral relativist said something like this, he would only mean "I think it is better, but you may not." However, I doubt any moral relativist would say something like this. More likely, it seems that a moral relativist would acknowledge the statement as vacuously true since the premise ("If you say that one set of moral ideas can be better") is false.

But the standard that measures two things is something different from either.

Considering moralities as a point in some geometric space, this is most likely, but it could also be that the standard is precisely one of the two things being compared. This minor point doesn't seem to invalidate the rest of the argument though.

The rest of the paragraph is a restatement of the two above points.

So, it seems most likely that one who disagrees with the conclusion would find it logically consistent but only vacuously true.

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    (1) You appear to be conflating validity and soundness; the question is about validity. (2) How does it follow that "the standard is precisely one of the two things being compared"? That seems necessarily false, or vacuous: the standard would always be better than anything not-it. – labreuer Jul 19 '14 at 3:57
  • It doesn't follow that "the standard is precisely one of the two things being compared." There are two cases: there are three things (morality A, morality B, and the standard), or there are two things (morality A which is also the standard, and morality B). – James Kingsbery Jul 21 '14 at 14:18

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