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A metaphor is like a simile.

Is there a name for the kind of statement that suggests an infinite recursion?

It is in a way similar to a paradox such as the one with a statement written on each side of a piece of paper. Side one says "The statement on the other side of this page is true"; Side two says "The statement on the other side of this page is false." But the quotation above is not a paradox, an endless contradiction, but an endless reinforcement. What do we call that?

I'm finding it hard even to come up with adequate tags for this question.

And remember: All generalizations are false.

Robusto
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    Could it be said to be a reciprocal clause? I'm not entirely sure if it's the same thing (or even if that's just something I made up)... – Andy F Jan 12 '11 at 16:08
  • @Andy: It sounds good, but I think it's made up hah. "Reciprocal" suggests there is some mutual relationship, not exactly recursion. – Noldorin Jan 12 '11 at 16:18
  • @Noldorin: Yeah, you're right, recursion is the more appropriate terminology. I think Zoot's got it right. – Andy F Jan 12 '11 at 16:34
  • @Andy F: Although I gave it an upvote, I'm not satisfied with Zoot's answer, since I'm already using the term "recursive expression" in the title of this question. I think there must be some other word that expresses this concept, though I can't for the life of me think of what it might be. My brain keeps offering me chiasmus but it's not really that. – Robusto Jan 12 '11 at 16:42
  • Well it's already described as recursion in the question, but yeah. I'm not sure there's an actual answer to this question. – Noldorin Jan 12 '11 at 16:43
  • Could it be petitio principii or the logical fallacy of "begging the question", also called a circular argument? Here's the wikipedia link: http://en.wikipedia.org/wiki/Begging_the_question – Tragicomic Jan 12 '11 at 16:55
  • @Tragicomic: If this were confined to the domain of logic I would say that had a chance. But I'm looking more for a literary or rhetorical term for this kind of figure. – Robusto Jan 12 '11 at 17:01
  • @Robusto: Wait, did I hear you say, in one of the comments below, that a simile is a type of metaphor? To my definition, this is not true. A metaphor replaces the original word; a simile is a phrase that contains the original word, at least implicitly—at any rate, it does not replace the original. If I had to draw them in a Venn diagram, I'd do it like this: OO – Cerberus - Reinstate Monica Jan 12 '11 at 18:54
  • @Cerberus: I was taught that a simile was a metaphor created by using "like" or "as": "My love is like a red, red rose" is a simile; "Let us not to the marriage of true minds admit impediments" is a metaphor. You could make the latter a simile by saying "The relationship of true minds is like a marriage, to which we should not admit impediments." – Robusto Jan 12 '11 at 19:14
  • @Cerberus: In fact, here's something on the subject from Wikipedia: "Metaphor also denotes rhetorical figures of speech that achieve their effects via association, comparison or resemblance (e.g., antithesis, hyperbole, metonymy and simile, which are all types of metaphor).[1]" – Robusto Jan 12 '11 at 19:17
  • @Robusto: Yikes, I have always thought that my definition was universal (what a surprise). If asked about "the relationship is like...", I'd say it was definitely not a metaphor. I see now that there is also a different school. But did you notice how you said "... is a metaphor"? That at least implies that you were comparing it subconsciously to a non-metaphor; so even if they overlap in theory, you would not let them overlap in practice. Oh, I don't know: I still feel very strongly that they do not even overlap in theory. But I suppose it is a matter of definition. – Cerberus - Reinstate Monica Jan 12 '11 at 20:09
  • @Robusto: Agreed, it is a matter of definition. Words either mean something or they don't. However fine you slice it, a simile is a type of metaphor. – Robusto Jan 12 '11 at 20:36
  • @Robusto: Okay, I've cheated. I have changed the article on Wikipedia. The paragraph you gave was based on someone's—probably unintentionally—misleading reference to the Oxford Companion to the English Language. I have looked it up, supplied the relevant text, and changed the paragraph accordingly. See what you think and change as you like. I have added "occasionally" to your definition because the OCEL calls it "not current" (see quote). Well, at least Aristotle would not have opposed you. http://en.wikipedia.org/w/index.php?title=Metaphor&action=historysubmit&diff=407533103&oldid=407383791 – Cerberus - Reinstate Monica Jan 12 '11 at 21:24
  • @Cerberus: You have finally wrestled this argument to the ground. If you mean to make this into a point-scoring game instead of a discourse, go with God. – Robusto Jan 12 '11 at 21:33
  • @Robusto: I'm sorry if I have offended you. My discussion here with you was mainly fuelled by a strong intuition I had. My change on the Wikipedia page I would have made anyway if I had ever stumbled upon it; this change was intended to make the paragraph accurately represent its only quoted source—without that footnote, I'd not have dared. I'll try to be less fanatical in discussions next time, I know I sometimes go too far. – Cerberus - Reinstate Monica Jan 12 '11 at 22:10

3 Answers3

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There's no recursion here, just self-reference.

It is not recursion (and certainly not "infinite recursion") because reading the sentence "A metaphor is like a simile" does not make you repeat/recurse on anything, nor does it invoke a smaller version of the same sentence, or anything like that. It merely so happens that "like a simile" is itself a simile. So this is just self-referential at most (it's not the sentence that refers to itself, but just the part "like a simile"), not recursive.

You may also consider the category of words that describe themselves (like "pentasyllabic"), sometimes called autological (though this is for words, rather than sentences), or (imprecisely) call your sentence self-descriptive, self-similar, or self-exemplifying. ("A metaphor is like a simile" is not an example of a metaphor — the subject of the sentence — but of a simile. But "A simile is like a metaphor" would be an example of a simile.)

Something related is sentences that describe themselves, known as autograms:

This autogram contains five a's, one b, two c's, two d's, thirty-one e's, five f's, five g's, eight h's, twelve i's, one j, one k, two l's, two m's, eighteen n's, sixteen o's, one p, one q, six r's, twenty-seven s's, twenty-one t's, three u's, seven v's, eight w's, three x's, four y's, and one z.

or

"This sentence contains five words."
"This sentence contains thirty-six letters."
"This sentence contains ten vowels."
"This sentence is written in English."
"This sentence contains precisely fifty characters."

or sentences that describe a part of themselves (from Douglas Hofstadter's Gödel, Escher Bach: An Eternal Golden Braid):

"Is composed of five words" is composed of five words.

(In your sentence it's the other way round: a part of your sentence, but not your sentence itself, describes the whole sentence.)

More from GEB:

This sentence is meaningless because it is self-referential.
This sentence no verb.
This sentence is false. (Epimenides paradox)
The sentence I am now writing is the sentence you are now reading.

The self-reference in most of these is achieved by directly using "this sentence" or equivalent; in your sentence it is achieved more subtly. (So "subtle self-reference" is another phrase that may work for your sentence.) GEB has an entire chapter on self-reference and self-replication; perhaps sentences of your type are mentioned there.

More links that may be amusing: essay, list, and "This Is the Title of This Story, Which Is Also Found Several Times in the Story Itself"

ShreevatsaR
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  • And yet "A metaphor is like a simile" is open-ended, since a simile is a type of metaphor. And self-reference is one definition of recursion. A procedure is recursive if one of the steps that makes up the procedure calls for a new running of the procedure. The example I quoted makes me run the definitions of simile and metaphor over and over again in my head. Am I the only one? – Robusto Jan 12 '11 at 17:50
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    This comment comes with an up-vote and says that your answer is informative and amusing, and it suggests adding a reference to Declarations in Speech Act theory. http://en.wikipedia.org/wiki/Speech_act#Illocutionary_acts – Cerberus - Reinstate Monica Jan 12 '11 at 17:52
  • @Cerberus: Thanks, that's interesting… so if I understand it correctly, declarations are (for our purposes) sentences like "I now pronounce you husband and wife" that become 'true' (or perform their function) by their own utterance? – ShreevatsaR Jan 12 '11 at 18:10
  • @Robusto: Self-reference is only part of recursion, not one of its definitions. I'm not sure what procedure the sentence "A metaphor is like a simile" specifies (if any), but it doesn't seem to involve a new "running" of the sentence itself. It seems that it must be isomorphic to the procedure that the sentence "A vehicle is like a bus" specifies. And the latter is clearly not recursive. (There is a difference—the latter relies on the meanings of "vehicle" and "bus", and the former on "simile" and "metaphor"—but the meanings don't depend on our sentence itself differently in the two cases.) – ShreevatsaR Jan 12 '11 at 18:12
  • @ShreevatsaR: Right, that is what it means. We could even broaden the scope of this phenomenon: if I say "you are stupid", I could rephrase that as "I say that you are stupid", which means practically the same; then we could say that this latter statement too was a Declaration, in as much that it became true by being pronounced—the highest-level predicate is "(I) say". // On second thought, this all isn't very relevant to the Question's example; it is merely another kind of self-reference. – Cerberus - Reinstate Monica Jan 12 '11 at 18:35
  • @ShreevatsaR: Who's to say I can't use the term recursion metaphorically? :-) – Robusto Jan 12 '11 at 19:23
  • I think I'm really asking the wrong question here, so I'm accepting this answer as providing a cogent response to what the phrasing of my question represents. But I'm going to try to formulate the real question that's in my mind, which remains unanswered. This is harder than I thought. Anyway, thanks. – Robusto Jan 13 '11 at 14:44
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I'd say the term you're probably looking for is circular definition.

But what you have there as an example isn't circular or recursive as I see it. It's a pretty straightforward statement with no dependencies. A metaphor IS like a simile, simple as that.

Now, if you said "a metaphor is like a simile" and I asked what a simile was and you said "a simile is like a metaphor," then you'd have a circular definition.

But if you're talking about the oddness of using the phrase "like a simile" which is in itself a simile, that's kind of self-referential, but not explicitly so. By that I mean that the self-reference doesn't involve the subject of the sentence. More explicitly self-referential would be where simile is the subject of the sentence and also involved in a simile: "a simile is like..."

bikeboy389
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  • +1 for "isn't circular or recursive as I see it. It's a pretty straightforward statement with no dependencies", and "kind of self-referential, but not explicitly so". Your answer came in while I was typing my long answer, and if I had seen it I wouldn't have posted so much verbiage. :-) – ShreevatsaR Jan 12 '11 at 17:29
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To understand recursion, you must first understand recursion.

I'd call it a recursive statement.

Zoot
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    Yes, I've seen that joke before. http://stackoverflow.com/questions/234075/what-is-your-best-programmer-joke/234868#234868. Pretty funny. And Google "recursion" sometime and it will ask you "Did you mean recursion?" – Robusto Jan 12 '11 at 16:15
  • Sorry, I don't think this is a recursive statement. Recursion and self-reference are related, but not the same. (Or rather, recursion always involves (a form of) self-reference, but not every instance of self-reference involves recursion.) – ShreevatsaR Jan 12 '11 at 17:26
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    a recursion is a recursion is a recursion is a recursion is a ... – Eldroß Jan 13 '11 at 08:52
  • Someone reboot Eldros! He's caught in an infinite loop! – Zoot Jan 13 '11 at 14:10