Hi, I'm new to this forum, and I'd like to bring in something I've done in another forum. I understand this might have been done in the How to defeat Ace and Smoker thread but this theory of mine doesn't only apply to them.
This has nothing to do with using the specific elemental's weakness against it, nor using the "spirit" which Shanks appeared to have used to defeat WB's men. I'm applying this theory to Logia-types in general, where physical attacks don't seem to have any effect on them. Also, this method does not involve using the Kairouseki, since other DF users would not have access to them.
I'll categorise this into 2 parts.
The first method of beating Logias can be seen in the Arabasta arc, where Luffy smashes into Ace and Smoker, thus dealing physical damage to them even though they have consumed Logia-type fruits. Therefore, I'll keep this simple, the first method is simply hitting them before they change into their respective element. Of course, most people probably already know this obvious trait, and so I'll move on to the..
This can also be seen in the Arabasta arc, Zoro VS Mr 1. In the midst of losing due to being unable to cut steel, Zoro remembers a teaching from his mentor about all things having a "Breath of life". In it, the sensei explains that there are swordsmen who can cut nothing, and because of their enlightenment, they can anything. Confusing? It was to me too, at first. Then the scene switches to Zoro swinging his ultra-sharp blade at a tree leaf without cutting it, and then, using similar amounts of strength, swinging it down on a rock and splitting it right in half.
Getting the picture? Zoro, by being able to feel the breath of all things, be it living or non-living, is able to cut any element he feels the breath of. The main condition is that, in being able to cut that element, he is unable to cut anything else other than that element. With that, he can do extra- powerful damage to an element without harming anything else along with it. Now to explain how this connects with Logia-types. As was explained by Zoro's sensei, all things have their breath of life, be it rocks, ice, fire, or even nothing. If you can condition yourself to cut that breath, then you can cut it. This is further enforced by a short response from Oda in an SBS: that Mihawk can cut the elements. In other words, to defeat a Logia type, what you cut is not his physical manifestation of the element, but the "breath of life" of the element he is currently changed into, and therefore you can cut the Logia-user as well.
What really enlightened me is found in one of the later chapters in the manga.
In the Zoro VS Kaku fight (i forgot which chapter, sorry), Zoro says that he will "break" Kaku's Tekkai first. In his mind, he had already intentioned to cut the metallic element that the Rokushiki-user possesses to minimise physical harm to his body, that is through the use of Tekkai. However, Kaku, in response, meets Zoro's blade WITHOUT turning on his Tekkai, stating that it was his own decision as to whether he wants to use his given ability or not. This confirmed what I had mentioned earlier; that you can cut whichever element you want in exchange for not being able to cut anything else.
In other words, despite all the existence of Logia-types in the world, there CAN still be such a person known as an "invincible" swordsman, one who IS able to defeat even a Logia user, even without the use of a Seatstone.
However, I don't think that this fact, that Logia-types can indeed be cut, limits to only swordsmen. If Luffy and the rest, or anybody for that matter, were to find out about the breath of all things, then they too would be able to beat Logia-users, using fists or legs alone. In fact, this is the reason, i feel, why WB can be conferred the title "The Strongest Man In The World" even if he doesn't possess the power of the DF (of course, we don't know yet if he does or not).
I don't know if I've hit the mark or not, but I think I'm pretty close.
It's an interesting theory, but a bit too farfetched for my tastes.