7
$\begingroup$

Is there a Latin phrase that would be used when accepting some statement without providing the proof of such a statement?

For example, say you are working on an elementary number theory proof, and you make the statement "since $p$ is odd, $p^2$ is odd, which we accept [Latin phrase for 'without showing proof']." Obviously this is a simple thing to prove, but in some cases it might be nice to acknowledge that a proof exists and we do not wish to show it.

Could ex facie be used in such a situation ("we accept ex facie that $q$ odd implies $q^2$ odd")? Or failing the existence of a Latin phrase, is there a way that sounds a little less crude than "without proof"?

  • 9
    Well, there is an English phrase. Why the need for Latin?2012-08-08
  • 2
    Why Latin? Using an uncommon foreign phrase only puts a burden on the reader to find out what the phrase means.2012-08-08
  • 8
    Why do you want it to be Latin? It will be much more readable simply to write something like "Let's assume as given that such-and-such" or "It can be proved that such-and-such".2012-08-08
  • 1
    "Accept without proof" sounds a little like "take as an axiom", which is not what you mean.2012-08-08
  • 1
    Quod gratis asseritur, gratis negatur.2012-08-08
  • 4
    The request for a Latin phrase is because I feel as if I've encountered one once upon a time, and I don't recall where -- just that I had to ask someone what exactly it was. Also, the English phrasing, "we state without proof that $q$ odd implies $q^2$ odd" seems a little patronizing, as similar wording is used in elementary textbooks for when a concept is deemed to complicated for the reader. I'm looking for a phrase that could be used in place of the dreaded "clearly," except that we acknowledge that proof of the statement exists, rather than hoping it does.2012-08-08
  • 15
    "The proof is left as an exercise for the reader".2012-08-08
  • 0
    ... a phrase which, apparently, goes back to Regiomontanus.2012-08-08
  • 2
    $$\begin{array}{l}\text{Caeli, Lesbia nostra, Lesbia illa,}\cr\text{Illa Lesbia, quam Catullus unam}\cr\text{Plus quam se atque suos amauit omnes,}\cr\text{Nunc in quadriuiis et angiportis}\cr\text{Glubit magnanimi Remi nepotes.}\end{array}$$2012-08-08
  • 8
    Just do what the author of my linear programming textbook does and claim that everything is "easy to see". As a bonus, it's a good way to make readers feel bad about themselves.2012-08-08
  • 2
    Why not "since $p$ is odd, $p^2$ is odd, which we **take for granted**..."2012-08-09
  • 2
    There is a list of Latin phrases, especially ones used in Mathematics, at http://www.mathacademy.com/pr/prime/articles/latin/index.asp, but I don't see anything there with the meaning you want. "Prima facie" is the closest ("since $p$ is odd, $p^2$ is prima facie odd") but I don't think that's quite right.2012-08-09
  • 0
    *prima facie* might be what I was thinking of... maybe that's why I had *ex facie* in mind. Interestingly, both seem to be legal terms used in a similar context.2012-08-09
  • 1
    If it's something as obvious as "if $p$ is odd, then $p^2$ is odd", then why tack on an awkward phrase? Just move right along to wherever you're really trying to get to, without skipping a beat. Tacking on something in Latin would look particularly goofy and pedantic. (If you feel you must, you might try some variation on "as is well-known" on for size.)2013-10-15
  • 0
    @user43208 Often times, the result may not be well known. For instance, when writing on dynamic game theory, one may wish to reference the conclusion of the Folk Theorem(s) without addressing the proof directly. Accepting the theorem *ex facie* streamlines the paper, but it also potentially elides quite a bit of important mathematics. Explicitly acknowledging that theorem exists and contains important, relevant results without also expounding on those results is, in my opinion, necessary for clear communication.2013-10-16
  • 0
    @Arkamis In such a case, I see there are two options here. One is to hunt down a reference for the folk result and cite it explicitly ("see lemma 1.4 in [2]"). When that is possible, that is by far the best thing to do: you are providing a service to the community who could benefit by knowing where now to find something they've vaguely heard. If you *can't* find a reference, then resort to something like "we assume without proof the following folk result..." and move along. What good does it actually do trotting out a somewhat obscure Latin phrase? It sounds very awkward to my ears.2013-10-16
  • 0
    Just trying to keep pace with the lawyers ;)2013-10-16
  • 0
    :-D Well, I'm not above a good "*ceteris paribus*" now and then either! Sometimes it's all in good fun.2013-10-16
  • 0
    "manifestly". [It's quite latin](https://en.wiktionary.org/wiki/manifest#English).2016-07-22

4 Answers 4

5

It appears as though ex facie bears the intended meaning. Prima facie has a similar meaning.

0

Arguendo is close, and might better fit proofs by contradiction, or derivations from a conjecture.

-1

Are you thinking of a priori?

  • 0
    This is not an answer - you should post it as a comment.2013-10-15
  • 1
    No. *A priori* means before the fact, which is different. The desired term instead would communicate that we're accepting a result on face value, without detailed examination that the result is true, perhaps because exploration would be a distraction from the intended result, or alternatively that demonstrating the result would be too lengthy. $${}{}$$As an example, consider writing a clever homework solution in an analysis class that uses, say, the Sylow theorems. You wouldn't want to prove them, but you might want to use them.2013-10-16
  • 2
    @DennisGulko look at the poster's reputation, it takes 50 reputation to post comments.2013-12-10
-1

Axiom (something that is accepted without proof) ex.: this statement is an Axiom.
Axiomatic, ex.: this statement is axiomatic in every sense.
Axiomatically, ex.: this statement is axiomatically accepted by some.
Note: Of Greek origin but surely used in Latin as well.