Why does Tosafot Do Two Tekhelet Strings

According to the Baal Hatanya’s Shulchan Aruch one follows Tosofot’s opinion on techelet as in 2 whole stings blue but tying like the Ari”zals method. I would like to know how Tosofot came to the idea that there are 2 whole strings becuase of the language in the possuk it would seem only 1 string would be blue I have searched your website but I cant seem to find any answer to my question besides some of the writing in Hebrew. My Hebrew isn’t the best for the time being so if it is possible can you give the reason why Tosafot and Rashi follow this way or even why the Sifri would follow this way?

Tosafot makes his opinion based on the Mishna (Men. 4:1) which states the tekhelet does not hinder (m’akev) the white and the white does not hinder the tekhelet. The mishna goes on to state that the head tefillin does not hinder the arm tefillin and the arm tefillin does not hinder the head tefillin. The statement concerning tefillin is understood to mean that if one has only of the tefillin pieces available, one can say the bracha and fulfill the mitzva of the component of tefillin by wearing that available piece – i.e., one need not have both, rather each one is a fulfillment of itself. The basic understanding of the mishna is that the same logic that applies to tefillin applies to the mitzva of tzitzit. That is, if one has only white or only tekhelet, the mitzvah is at least partially fulfilled with the one available component. This leads Tosafot to hold that just as the head tefillin is equal to the arm tefillin, so too the tekhelet strings are equal to the white strings – meaning each should be represented equally in number. As to the question of the pasuk “and you shall place on the tzitzit of your corner a PTIL tekhelet”, though the standard translation of “ptil” is “strand” there is support for the word “ptil” carrying the meaning of “tassel” – i.e., multiple strands.

Regarding the Sifri which states that in fact there should be 2 white and 2 tekhelet strands – the Gra calls this version into question.

– Mois Navon.

Mois Navon