Responsa for Shabbat 2:3
כָּל הַיּוֹצֵא מִן הָעֵץ אֵין מַדְלִיקִין בּוֹ אֶלָּא פִשְׁתָּן. וְכָל הַיּוֹצֵא מִן הָעֵץ אֵינוֹ מִטַּמֵּא טֻמְאַת אֹהָלִים אֶלָּא פִשְׁתָּן. פְּתִילַת הַבֶּגֶד שֶׁקִּפְּלָהּ וְלֹא הִבְהֲבָהּ, רַבִּי אֱלִיעֶזֶר אוֹמֵר, טְמֵאָה, וְאֵין מַדְלִיקִין בָּהּ. רַבִּי עֲקִיבָא אוֹמֵר, טְהוֹרָה, וּמַדְלִיקִין בָּהּ:
Whatever issues from a tree is not used for kindling [i.e., to make a wick of it] except flax, [which is called a "tree," viz. (Joshua 1:6): "And she hid them among the tree-flax," in spite of which we kindle with a wick made from it. And hemp and cotton do not issue from a tree, but are kinds of seed, for which reason they are kindled with. And flax, too, is a kind of seed, and is added (as being permitted) only because it is called a tree, viz.: "And she hid them among the tree-flax."] And whatever issues from a tree does not produce tent-uncleanliness [(If one made a tent of them, and the dead body were under it, it is as any other house and does not require sprinkling and immersion; for the tent itself does not acquire uncleanliness, but only the vessels under it.)] except flax, [in which instance the tent itself becomes unclean, it being written (Numbers 19:18): "And he shall sprinkle on the tent"; and it is derived (by identity) "tent" - "tent" from what is stated in respect to the Tabernacle, viz. (Exodus 40:19): "And he spread the tent upon the tabernacle." And in the tent of the tabernacle there was nothing that issued from a tree but flax, viz. (Ibid. 26:1): "ten curtains of twisted flax."] A wick (made from) a garment, which was twisted, but not yet singed [on a flame for proper kindling (We are speaking of a garment fragment which is exactly three by three fingers)] — R. Eliezer says: It is unclean, and we do not kindle with it. R. Akiva says: It is clean, and we kindle with it. [("It is unclean":) For its having been twisted does not remove it from the status of "garment," its not having been singed. ("It is clean":) Its having been twisted removes it from the status of "garment," so that it is as if it lacks three by three fingers; and anything less than that size acquires neither plague-uncleanliness nor dead-body uncleanliness. ("and we do not kindle with it":) We are speaking of a festival which falls out on Sabbath eve, where the interdict of muktzeh obtains, and we cannot kindle with pieces of articles (kelim), which were broken on that day, for this would be "nolad" (lit., "born" on that day). But we can kindle with (complete) articles, for it is permitted to move them. And all hold that one must light most of the wick emerging from the lamp before he removes his hand. Thus, the rationale of R. Eliezer, who says that we do not kindle with it: Its having been twisted does not remove it from the status of (a complete) "article," so that when he lights a little of it, since it is exactly three by three, he renders it a piece of an article (for less than three by three is not an article), and when he lights it with his hands to complete (the requirement of lighting) the majority of what issues forth (from the lamp), he is found to be lighting a piece of an article which was broken on the festival (for when we say that it is permitted to light articles, this is only when they are not touched after they are reduced in size). And R. Akiva says that we may kindle with it. He holds that its having been twisted removes it from the status of "article." And he twisted it on the eve of the festival, for it is not permitted to twist a wick on a festival. Therefore, we do not have a piece of an article which was broken on a festival, and it is permitted to kindle with it. The halachah is in accordance with R. Akiva.]