Kiddushin

In business dealings, the witnesses know what is happening, but in silence, he may be buying something, paying off a debt, or giving a gift. So how do the witnesses know that it is a kiddushin?

When it is clear from the context that they mean Kiddushin or when the couple told them that it would be given for Kiddushin.

I understood that there are three methods of saying something in Kiddushin. One method is that the saying makes the Kiddushin. A second method is that the saying is not essential, but is so that the Kiddushin will not be things of the heart, and therefore if it is clear from the context or someone was told that it will be given for Kiddushin, even without saying something, the Kiddushin will be perceived. And a third method is the Mordechai method, which is that even saying something out of the heart is not necessary. According to the Mordechai method, how can one testify to the Kiddushin?

I didn't understand what you didn't like about what I wrote. It's clear that you need the intention to sanctify. No one gives up on that.

It is clear that intention is required, but according to Mordechai, it does not need to be expressed outwardly. The rabbi wrote that one can testify to the consecration when it is clear from the context or the couple told the witnesses. But according to Mordechai, even that is not necessary. The couple's intention is sufficient. If it is clear from the context or the witnesses were told, this is the second method that I wrote, not Mordechai. In the case that Mordechai is talking about, how can the witnesses testify to the consecration if the couple's intention is not clear (even though the couple knows what they meant) assuming that Mordechai disagrees in a real case and not theoretically, it is possible to consecrate in silence if the witnesses could read minds.
Now I thought that there might be a certain sign that only the witnesses recognize that shows that it is a consecration, and then it is still a consecration in silence that would benefit only Mordechai and not those who disagree with him. Does this seem like a good solution to the rabbi?

I don't know what this sign is. It's hard for me to believe that Mordechai means when there is no evidence from the circumstances that the intention is for kiddushin. Although, from the simplified language of Rama 27:33, it seems that no sign is really needed and the couple's confession is sufficient. Perhaps his intention is to say that if both confess, then this is a confession by the Ba'd and Shishiba as two witnesses to the fact that the matter has taken place (and there is a known disagreement between Kitzvah and Rashba on this).

I meant that the witnesses are friends of the man and know that he touches his hair every time he sanctifies, and then only Mordechai will say that the sanctification is perceived because those who disagree with him will say that it is matters of the heart (because touching the hair is not a normal sign of sanctification and this is clear only to his friends). But the rabbi's solution is better because it does not seem reasonable to me that Mordechai would disagree in such a case. Thank you.