Between Two Worlds

It's common in some circles to suggest that the apostle Paul didn't really write some of the letters that are now ascribed to him. Ray Van Neste, writing the introduction to 1 Timothy in the ESV Study Bible, has a concise explanation of why the pseudonymity solution is untenable:

Additionally, it is problematic to argue that these works were written under a false name since the early church clearly excluded from the apostolic canon any works they thought to be pseudonymous. While critics point to the common practice of pseudonymous writing in the ancient world, they usually fail to point out that this practice, though common in the culture, was not common in personal letters, and was categorically rejected by the early church (cf. 2 Thess. 2:2; 3:17; also Muratorian Canon 64–67; Eusebius, Ecclesiastical History 6.12.3). Tertullian (c. A.D. 160–225) wrote that when it was discovered that a church elder had composed a pseudonymous work, The Acts of Paul (which included a purported Pauline letter, 3 Corinthians), the offending elder “was removed from his office” (On Baptism 17). Accepting as Scripture letters that lie about their origin is also a significant ethical problem. Thus, there is a good basis for affirming the straightforward claim of these letters as authentically written by Paul.

For more on this, see D.A. Carson's essay, “Pseudonymity and Pseudepigraphy,” in Dictionary of New Testament Background, ed. Craig A. Evans and Stanley E. Porter (Downers Grove: IVP, 2000), 857-64.

Brief Postscript: I should mention one other brief but important point. Sometimes in an issue like this we tend to look first at the external evidence (e.g., whether or not pseudonymity [false naming] or pseudepigraphy [false attributing] were accepted practices in the first centuries). But we sometimes ignore the internal evidence within the NT letters themselves. For example: