The Gemora states that testimony is valid only from the mouths of the witnesses, not on the basis of any documents. It is evident that writing is not the same as talking.
The Gemora Chagigah (10b) cites Shmuel who states that one who resolves to make a vow must express the vow with his lips; otherwise, it is meaningless.
The Noda b’Yehudah (Y”D I: 66) inquires if an oath that was written down but not expressed would be valid as an oath. His underlying question is: Do we regard his written word as an expression of his lips?
This should be dependent on a dispute between the Rambam and Rabbeinu Tam regarding the validity of testimony from a written document. The Rambam maintains that testimony must be from the mouth of the witnesses and a document will not be Biblically acceptable for testimony. Rabbeinu Tam disagrees and holds that one who is physically capable of testifying may testify through the means of a document.
He concludes, however, that even the Rambam would agree that writing is considered testimony and yet, a written document cannot be accepted by Beis Din. The logic for this is as follows: An act of writing can constitute speech, but only during the time that it is being written. Beis Din will only accept an oral testimony when they hear it directly; hearsay is disqualified. Witnesses who signed a document are testifying, but Beis Din is not present at that time. If they would sign in front of Beis Din, that would be considered valid testimony.
With this principle, you can answer what would seemingly be a contradiction in the Rambam. He rules in Hilchos Eidus (3:7) that testimony must be from the mouth of the witnesses and a document will not be Biblically acceptable for testimony; yet later in Perek 9:11, he writes that one is required to testify with his mouth or at least that he is fitting to testify with his mouth. This would imply that if he is fitting to testify with his mouth, he would be permitted to testify through the means of a document. According to the Noda b’Yehudah’s explanation, it can be said that the Rambam allows witnesses to testify through the means of a document, but only if they sign the document when Beis Din is present. Accordingly, we can say that an oath taken through writing will be binding.
Reb Akiva Eiger discusses some other practical applications for this principle.
(http://weeklyshtikle.blogspot.com/2007/05/weekly-shtikle-emor.html) The Weekly Shtikle writes the following: The topic is the discussion as to whether or not writing may qualify as a valid means of fulfilling the mitzvah of Sefiras HaOmer. That is, if one was to write, "Hayom Yom X La'Omer," would that be sufficient to fulfill one's obligation and would this action disallow one from repeating the count with a brachah?
The discussion of this halachic quandary follows an interesting family tree. This issue is first dealt with in Shaalos uTeshuvos of R' Akiva Eiger, siman 29. The teshuvah is actually written by R' Akiva Eiger's uncle, R' Wolf Eiger. Unable to attend his nephew's wedding, he made a simultaneous banquet of his own to celebrate the occasion. He wrote to his nephew about this halachic issue which was discussed at the banquet. He cites a number of related issues which he builds together to try to reach a conclusion. The gemara (Yevamos 31b, Gittin 71a) teaches that witnesses may only testify by means of their mouths and not by writing. The gemara (Shabbos 153b) states that mutes should not separate Terumah because they cannot say the brachah. It is assumed that writing the brachah would not have been sufficient. Also, there is a discussion amongst the commentaries with regards to the validity of a vow that is written and not recited. R' Wolf Eiger concludes that writing is not a sufficient means of fulfilling the mitzvah of Sefiras HaOmer. However, this sparks a debate between him and his nephew which stretches out to siman 32.
This issue is eventually discussed in Shaalos uTeshuvos Kesav Sofer (Yoreh Dei'ah siman 106) by R' Avraham Shmuel Binyomin Sofer, R' Akiva Eiger's grandson who was, in fact, named after R' Wolf Eiger. He covers a host of related topics and eventually discusses the exchange recorded in his grandfather's sefer. The debate, although it encompasses various pertinent issues, never produces any concrete proof directly concerning the act of counting. However, Ksav Sofer quotes his father, Chasam Sofer, in his footnotes to Shaalos uTeshuvos R' Akiva Eiger (his father- in-law) where he provides a more concrete proof. The gemara (Yoma 22b) teaches that one who counts the number of B'nei Yisroel transgresses a prohibition as it is written (Hoshea 2:1) "And the number of B'nei Yisroel shall be like the sand of the sea that shall not be measured nor counted." The gemara cites two examples (Shmuel I 11:8, 15:4) where Shaul HaMelech went out of his way to avoid this prohibition by using pieces of clay or rams in order to perform a census. Chasam Sofer suggests that Shaul could simply have counted the men by writing down the numbers and not saying them. Since Shaul went to far greater lengths, we are compelled to say that writing the number of men would still have qualified as counting them and he would hot have sufficiently dodged the prohibition. Thus, concludes Chasam Sofer, if one has explicit intention to fulfill the mitzvah, writing is a valid means of performing the mitzvah of Sefiras HaOmer. However, Kesav Sofer suggests that perhaps the brachah should not be recited in this case.
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