This is essentially about William Lane Craig's publications on (his version of) the Kalam cosmological argument. Craig is constantly talking about "absurdities" that result from considering infinite quantities. In plain English, that term and its derivatives have very ambiguous and squishy meanings. For instance we might say that "fairies are absurd," by which we mean that we just subjectively find the idea to be ridiculous or silly. But Craig seems to be using the word in a different way, as if it has something to do with metaphysical impossibility. Here's an example (one of many!) of how he employs the term:

"Hilbert’s Hotel is absurd. But if an actual infinite were metaphysically possible, then such a hotel would be metaphysically possible. It follows that the real existence of an actual infinite is not metaphysically possible."

That's from his refereed article in The Blackwell Companion to Natural Theology (2009), although he repeats it verbatim in various other places. As far as I can tell, it's just an invalid argument. In particular, Craig is unequivocally mistaken that his conclusion follows as he claims it does---unless of course the word "absurd" means something specialized, and entails in some way metaphysical impossibility. But I can't find that term ever defined or characterized in such a way, not even in Craig's own writings.

What do you guys think? Is Craig wrong that his conclusion follows from the premises? Or does the word "absurd" have some specialized meaning in philosophical discourse? Or something else that I'm missing?


EDIT: After receiving some curious responses, I think perhaps I've been unclear about my question. So here's my attempt at clarification:

Obviously, Craig is taking "absurd" to mean something that entails metaphysical impossibility. So, his argument as quoted isn't invalid when interpreted as such. Instead, my question could be rephrased as follows:

Is Craig's exposition of the argument precise and unambiguous?

Unless the term "absurd" has some specialized meaning in philosophy, then it seems the answer is no. In that case, it would be (IMO) unclear exactly what Craig means. But if "absurd" does have a specialized meaning, then I'd like to know.

  • 2
    Generally, "absurd" means something close to contradictory, incoherent, although often in a sense looser than strictly logically contradictory (there is another use of "absurd" by existentialists, which is not relevant here). It can be pragmatically impossible, or inconsistent with background assumptions taken as uncontroversial. In Craig's case, as you point out, it means "contradictory to Craig's metaphysical intuitions". So his argument is perfectly valid, not that it does much for those who do not share his intuitions.
    – Conifold
    May 5, 2020 at 10:34
  • @Conifold So, in maths for instance, we'll sometimes use the word "absurd" in our exposition as a stand-in for "contradiction," or something like that. But in these cases it's always clear from context what we mean. We'll also use other cutesy ways to make reading our papers less tedious---but again, this never happens at the cost of clarity. In the case of Craig, it's really not clear to me what he means. That could be because I'm inexperienced. And I don't think he means what you said, because then his conclusion still wouldn't follow.
    – Ben W
    May 5, 2020 at 11:00
  • 1
    Welcome to philosophy, as opposed to math (although, if we are honest, hand waiving does happen even in math papers routinely). Problems are not as precise, criteria of validity are not as sharp, and mathematical level of rigor can not be expected even in physics, let alone in philosophy. It is expected that the use of terms is clarified (as far as possible) by context and examples, but again, this is an unattainable ideal even in math. And some are more responsible with it than others.
    – Conifold
    May 5, 2020 at 11:25
  • It might help to look at the word origin. 'Ab surditas' means "from deafness". An absurdity is the kind of thing that, even if it were true, we are not equipped to understand. We can't say it is false, we just know that it cannot make sense to us. (It was used for math problems with irrational solutions, before the acceptance of irrational numbers. You could prove you would not be able to express the solution in numbers, even if/though it existed.) May 8, 2020 at 13:43

5 Answers 5


Hilbert's paradox of the Grand Hotel is a good example: it is called "paradox" because illustrates a counterintuitive property of infinite sets.

Thus, we can call it "absurd" because it is at odds with our intuition: in our experience there are no infinite Hotels.

But, form a logical point of view, it is not a contradiction because it is consistent with the mathematical theory of infinite sets.

IMO, Craig uses the word "absurd" to mean "contradictory". Craig's argument is:

"if an actual infinite were metaphysically possible, then Hilbert's hotel would be metaphysically possible. [But Hilbert's hotel is contradictory, and thus it is not metaphysically possible (and a fortiori not existent.] It follows that the real existence of an actual infinite is not metaphysically possible."

Philosophy is full of "paradoxes", that are absurd (devoided of sense, meaningless) because they are counterintuitive, but not all of them are contradictions.

Maybe none: maybe for each one of them we can find an odd, but not "metaphysically impossible", situation where they have sense.

Consider e.g. Moore's paradox: we can imagine a "real" situation where the statement:

"p, but I believe not p"

is not senseless: I'm leaving in the Middle Ages, where knowledge and belief of Bible is widespread and p is a shorthand for "some prophet brought a dead boy back to life", but I'm an atheist.

And we may find also odd situations for the statement "I am asleep now" (I'm a somnambulist) and "I am dead" (an horror novel, a testament).

[All previous examples are due to Joseph Agassi.]

Even the well-known Liar paradox is a contradiction when we try to formalize it in a "logical perfect" formal language.

As originally formulated by Epimenides in his poem Cretica (Κρητικά, quoted twice in the New Testament),

[Minos addresses Zeus thus:] They fashioned a tomb for you, holy and high one,

Cretans, always liars, evil beasts, idle bellies.

it his perfectly intelligible: it is not meaningless at all.

  • Does Craig ever lay a specific pair of propositions which are clearly contradictory but he thinks are both implied by the Hilbert's hotel scenario? As argued on p. 7 here, "If Hilbert’s Hotel were said to be both fully occupied and not fully occupied, then it would be a contradiction.Similarly if it were said that Hilbert’s Hotel both could and could not accommodate an additional guest, then it would be a contradiction." But neither pair are actually implied by the scenario.
    – Hypnosifl
    May 20, 2020 at 15:47

There is a form of logical proof that a proposition is false called reductio ad absurdum or reduction to the absurd. Typically, a given proposition is shown to lead to two mutually contradictory conclusions. This is clearly absurd and so the proposition must be false.

This is the usual sense in which a philosopher means that something is absurd, although the English language being what it is, the occurrence of other usages may not be ruled out. For example the "absurd" has a special role to play in existentialism.


While @Conifold correctly notes that the term “absurd,” as used in both mathematics and [often] analytic philosophy is not directly relevant to its use in existential philosophy, there are some parallels that your question [and the example you site] would seem to address, precisely relating to the ambiguity of the term that permits it to be used in all three language games.

Accepting the idea that “philosophy begins in wonder,” existentialists argue that human beings cannot escape asking the question, “What is the meaning of existence?” They deny, however, that there is an answer to this question, and reject every scientific, teleological, metaphysical, or human-created end that purport to provide an adequate answer.

For instance, Sartre posits/presupposes that “existence precedes essence.” Thus while the meaning of life question seeks an a priori metaphysically universal, “why are we here”, “meaning of it all,” answer “from the beyond,” so to speak, no such answer can exist because there is nothing [knowably] there that can provide it (given the presupposition). Or see Camus’ take (from https://plato.stanford.edu/entries/camus/):

Thus, while accepting that human beings inevitably seek to understand life’s purpose, Camus takes the skeptical position that the natural world, the universe, and the human enterprise remain silent about any such purpose. Since existence itself has no meaning, we must learn to bear an irresolvable emptiness. This paradoxical situation, then, between our impulse to ask ultimate questions and the impossibility of achieving any adequate answer, is what Camus calls the absurd. Camus’s philosophy of the absurd explores the consequences arising from this basic paradox

Camus’s understanding of absurdity is best captured in an image, not an argument: of Sisyphus straining to push his rock up the mountain, watching it roll down, then descending after the rock to begin all over, in an endless cycle. Like Sisyphus, humans cannot help but continue to ask after the meaning of life, only to see our answers tumble back down.

Thus, unless one [believes in a transcendental “God” or] can provide a demonstrably true functional definition of what it is to be a [wo]Man, ala Alasdair MacIntyre’s in After Virtue (1981) [as opposed to simply a physicalist/mechanistic definitions] of Man, it is arguably as “absurd” or “incoherent” [given the operative presuppositions of the physicalist/mechanistic descriptions] to ask “why are we here”, or “what is the meaning of life,” as it is for a mathematician who is a metaphysical skeptic to ask, for instance, “what is a number?”

  • What is the link with Craig's assertion that "the real existence of an actual infinite is not metaphysically possible" ? May 18, 2020 at 13:07
  • @Mauro ALLEGRANZA: I am not sure I understand the question. Although, I I am no mathematician or logician, so I might have a gaping blind spot. My point was simply that absurdities all seem to entail, as you mention in your answer, contexts, presuppositions and intuitions. For instance, see here: philosophicaldisquisitions.blogspot.com/2013/08/…. Please note that I lack the epistemic stamina, conceptual tools and interest/curiosity to peruse and defend/attack the arguments made there in a robust manner, so don't ask.
    – gonzo
    May 18, 2020 at 17:51

(1) Let's admit that " absurd" means " contrary to reason".

(2) Now, as says Leibniz, there are 2 "grand" principles of our reasonings : the principle of non-contradiction and the principle of sufficient reason.

(2) So, there are two ways for something to be absurd

  • being contradictory

  • having no reason, no justification.

When I was a student, there was a guy at the university that, in winter, wore in a usual manner a jackett and a football short. Maybe was it absurd in both ways.


A conspicuous claim of the argument Craig raises is that the argument is up to the contemporary standards of philosophical rigour. To that end, he allegedly obtains a metaphysical impossibility by a pragmatic absurdity. He uses the word 'absurd' ambiguously, denoting/connoting in turn the ordinary sense of exceedingly unreasonable and the logical sense as in the method of reductio ad absurdum.

Admittedly, reductio ad absurdum, reductio ad falsum, reductio ad contradictionem, and often, reductio ad impossibile amount to the same judgement in tradition and indistinctive contexts of contemporary philosophy. However, we have learnt to sensibly engage with both impossibility and contradiction (consider Hegelian metaphysics, dialethic logic, etc.) and make precise distinctions if the context demands, and Craig's assertive context demands.

In my opinion, the primary philosophical significance of an argument for or against the existence of God lies not in its convincing power, but in its contribution to refining our thought. In this respect, Craig's argument seems not a step forward.

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