I read an article of a case where a daughter was marrying her mother under the now SSM law.

Josephus,

Do you have a link to this article?

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Suggesting that polygamy or incestuous relationships would be next, if same-sex marriage were to be legislated for, is indeed the slippery slope fallacy.

The Slippery Slope argument is fallacious when it is used to appeal to extreme hypotheticals instead of addressing the issue at hand. Particularly when no logical reason is given for the inevitability of the extreme hypotheticals.

In no way does the size of the initial step make a difference to whether the argument is fallacious, this is something the OP has made up.

http://yourlogicalfallacyis.com/slippery-slope
http://www.logicallyfallacious.com/tools/lp/Bo/LogicalFallacies/162/Slippery-Slope
http://en.wikipedia.org/wiki/Slippery_slope

So, no, it’s not a “false argument” at all.

CE,
I could have added that the only reason for homosexuals wanting the word marriage is to steal some of our good reputation that the homosexuals do not have. Their antics at the Sydney gay madi gras show they have not earned it.

«I read an article of a case where a daughter was marrying her mother under the now SSM law.»

Of course, the author has to make a living...

Anyway, since when do human-made laws determine whether one is married or not?

//I could have added that the only reason for homosexuals wanting the word marriage is to steal some of our good reputation//

You don't have a good reputation, Banjo.

Dear Josephus,

A daughter marrying her mother - under SSM laws?
That would be quite extraordinary in this country
because in our Marriage Act the marrying of relatives is
forbidden.

Every society has an incest taboo, a powerful moral
prohibition against sexual contact between certain
categories of relatives. But although no society allows
people to mate with anyone they choose, different
societies have quite different ideas about who might
be a prohibited marriage partner.

In the US for example, all fifty states prohibit marriage
between a person and his or her parent, grandparent,
uncle or aunt, brother or sister, and niece or nephew;
an additional twenty-nine states regard marriage between
first cousins as incestuous, but the remainder do not make
any distinction between siblings (brothers and sisters) and
cousins.

In these societies there are usually no separate words for
"brother" and "cousin": they are regarded as the same kind
of relative, and the incest taboo is therefore extended to
first, second, third, and even more distant cousins as well.

A few societies actually extend the taboo to social as well
as sexual behaviour. Among the Nama Hottentots, an adult
brother and sister could not be alone together or even
speak to one another, and a Crow husband could not talk to
or even look at his mother-in-law.

Some cultures, on the other hand, are very specific about whom
people may or should marry, as well as whom they may not.
Therefore, although certain societies consider it incestuous
to marry a child of one's mother's sister, or of one's father's
brother, they may expect - or even require - that one should
marry a child of one's mother's brother, or of one's father's
sister. Biologically, of course, each type of cousin is
equally close; but social norms define one union as
revolting, the other as desirable.

Where did you read about the case that you cited - and in
which country did this happen?