# Use of se ... tiam ... in logical statements

When writing mathematics or logic, one uses the construction "if A, then B" such as "if triangle ABC is equilateral, then its angles are all equal". I know the translation is se A, tiam B. But I find tiam a little jarring, as it is supposed to be specifically temporal, while in the sentence above, the triangle is equilateral independent of time. It doesn't suddenly have all equal angles, it always had all equal angles. In a phrase such as "if the weather is good, then we will go camping", the temporal meaning is the right one. I know I could drop tiam and just say se A, B, but mathematicians on purpose put "then" in the construction as the hypothesis can be complicated including having several commas, so you need some word to say when hypotheses (A) stop and the conclusion (B) begins. So the question is, is there another solution that doesn't bring in time? Or is tiam always used even in this context, and I should get over my unease about it.

The most common word to indicate the conclusion of a se-phrase is tiam, and it doesn't have a temporal meaning when used in this function. So you can use it without qualms.

Some authors also use do instead of tiam in this function, but it is much less common, and not supported by Zamenhof's usage. Here are two examples from the Tekstaro de Esperanto:

• Se A estas B, do ankaŭ B estas A.
• se du sistemoj A kaj B termike ekvilibras kun la tria sistemo C, do ili nepre termike ekvilibras inter si.

The usage of tial in this function seems to me to be non-existent, or at least even much less common than do. So if you feel the urge to avoid the common tiam, and just dropping it is problematic, go for do. But really there is no reason to avoid this common usage of tiam.

The translation of tiam even in its temporal sense can be considered appropriate here. As the PMEG states, tiam is "en tiu tempo / en tiu fojo" i.e. "in that time / on that occasion".

The "if" in your construction is essentially "in the event that..." or "on the occasion that...". It sets up the definition of a scenario, and when that scenario is true, then the conclusion follows.

Perhaps because of the definition stretching this far, Zamenhof didn't see the need in complicating things by changing the ti- word usage under this scenario?

The relationship se - tiam seems to be well established in Mathematical terminology. See this page for example.

http://www2.cs.upb.de/extern/fb/2/Kyb.Paed/INT/01-int.htm

I asked Francisko, who often lectures on mathematical topics at the Aŭtuna Renkontiĝo de Esperanto and who has an in-depth knowledge of mathematical terms in Esperanto, and he replied with the following example.

• Ekzemple: se x = 0, tiam 2x = 0.

In his dictionary J.C. Wells gives tial for 'therefore'; that might be a better fit in this context, as it expresses the cause rather than the chronological aspect as tiam does.

• The usage of tial in this meaning is practically non-existent. As explained in my answer, one can use do, but there is really no reason to avoid the much more common tiam. Nov 2 '16 at 11:28

The most common word is tiam (directly mirroring the English "then") but you can use do ("therefore"), and maybe tial ("because of that") e.g. Se la kondiĉoj teniĝas, tial..., and even tie in the form En la okazo kie X, tie...

There are plenty of other ways to phrase it:

• X [logike] implicas ke Y.

• Se X, sekvas ke Y. Se X, sekve Y.

• El/de X, sekvas ke Y.

• Se X, tiukaze/tiuokaze Y.

• Se X, dedukteblas/indukteblas ke Y.

• Se X, konkludeblas ke Y.

• Se X, la sekvo/konsekvenco/rezulto estas ke Y.

And for "if and only if":

• X se kaj nur se Y.

• X implicas ke Y, kaj inverse.

• X estas necesa kaj sufiĉa kondiĉo de Y.

• Are your answers here examples of use from actual mathematical texts? Se... tial, it turns out, is not at all common and often means something different. Nov 2 '16 at 14:02
• The examples given above are all correct. Nov 2 '16 at 15:12
• I certainly didn't mean to suggest that you would use incorrect examples on purpose. I would contend (as others have) that se ... tial, as just one example is in fact not correct. My question is where did these examples come from. Are you quoting from somewhere or are they your own? Nov 2 '16 at 15:21
• These are straightforward examples of how logical implications can be expressed in Esperanto. I remember them from reading. If you like, I can google specific examples. It is hard to google se X, tial Y but it is valid when X is the cause of Y. Nov 2 '16 at 16:55

Even if “tiam” is not strictly correct, it is convenient to override its literal meaning with the “logical” meaning in such contexts. Convenience rules as strongly in mathematical / logical contexts as elsewhere, and this particular convenience is far less qualms-giving than the practice of using “if...then” in definitions to mean “if, and only if,” – for example: definition: if an integer x > 1 has only 2 positive integer divisors, then x is a prime”.