On the other hand, this fairly short text has a surprisingly dense number of allusions (and even quotations) from New Testament traditions. Polycarp cites synoptic Jesus tradition in Phil. 2.3, though the precise relation to Matthew 7 and 5 (as well as other texts) is somewhat complicated:
[B]ut instead remembering what the Lord said as he taught: "Do not judge, so that you may not be judged; forgive, and you will be forgiven; show mercy, so that you may be shown mercy; with the measure you use, it will be measured back to you;" and, "blessed are the poor and those who are persecuted for righteousness' sake, for theirs is the kingdom of God." [see my comments in a previous post]
Polycarp also refers explicitly to Paul on a couple occasions (3.2; 9.1; 11.2–3) and echoes traditions found in 1 Peter in Phil. 10.2. Of course, Polycarp also refers to both the letters and the person of Ignatius. Finally, Polycarp also cites Ephesians in Phil. 12.1.
In other words, while Polycarp exhibits very little interest in Moses and the Torah or any of the prophetic or other writings, he does seem very interested in the traditions and/or texts that we now refer to as the New Testament. Polycarp does not yet provide evidence of an awareness of any "canon" of NT texts, but the conjunction of citations and allusions, along with the reference to Eph 4.26 at 12.1 and the reference to these as "scriptures" [sacris literis; scripturis], raises some very interesting questions.
[NB: In looking back over Michael Holmes's introductory comments to Philippians, I noticed that he appraises Polycarp's use of Hebrew biblical texts and traditions very differently than I have. Holmes says, "[Philippians] reveals, in addition to a direct and unpretentious style and a sensitive pastoral manner, a deep indebtedness to the scriptures (in the form of the Septuagint); specifically, he apparently draws upon Psalms, Proverbs, Isaiah, Jeremiah, Ezekiel, and Tobit" (2007: 272–3). Clearly I've missed something. I don't see how Polycarp has made use of any of these texts, but I would trust Holmes here rather than myself. (In addition, Holmes refers to W. R. Schoedel's study, Polycarp, Martyrdom of Polycarp, Fragments of Papias, vol. 5 of The Apostolic Fathers, ed. R. M. Grant [Camden, NJ: Nelson, 1967], 4–5.)]