Born in Kilkenny, and also known as Mac Giolla Cuddy, or Arsdekin. He studied theology at Louvain, and then became a Jesuit at Mechelen in 1642. He taught philosophy, moral theology, and scripture at Louvain and Antwerp, and several of the theses over which he presided were printed and are listed below. He wrote a treatise in English and Irish on miracles. His Theologia Quadripartita, a guide to essential Catholic teachings and controversies with Protestants, was extremely popular, quickly selling out, and he produced an expanded form of the work in the same year, the Theologia Tripartita. The work received censure from the Inquisition and was thus emended at various points during the production of subsequent editons. Brussels MS 7299, f.71r-75v contains a summary of things to be emended by Archdekin. He also published a life of St Patrick accompanied by the so-called Prophecies of St Malachy, and a treatise "de constantia Hiberniae in religione Romana inter persecutiones poeneis perpetuas, per annos mille ducentos". At his death, he left a manuscript entitled “Theologia Apostolica”. The titles below scarcely convey the popularity of Archdekin’s works, which were reissued many times despite the earlier censure.
1. Theses Sacrae in Epist. Pauli Ad Romanos et Primum Ad Corinthianos (Louvain, 1668).
2. Theses Sacrae in Sancta Jesu Christi Evangelia, (Louvain, 1669), Quarto.
3. Praecipuae Controversiae Fidei Ad Facilem Methodum Redactae (Louvain, 1671), Octavo.
4. Theses Sacrae de Verbo Dei et Creatione Mundi (Louvain, 1671), Quarto.
5. Vitae et Miraculorum Sancti Patricii Hiberniae, Apostoli Epitome Cum Brevi Notitia Hiberniae et Prophetia S Malachiae (Louvain, 1671), Octavo.
6. Theses Theologicae de Deo Uno et Triuno ([Antwerp], ), Quarto.
7. Apparatus Materiae et Formae Pro Doctrina Sacra in Quavis Dictione Facile Methodo Paranda, et Pro Catechesi Cum Exemplis Illustranda. Cum Praxi Varia Assistendi Aegris Ac Moribundis, et Alias Functiones Sacras Rite Obeundi, (Antwerp, 1678), Octavo.
8. Theologia Quadripartita (Prague, 1678).
9. Theologia Tripartita Universa, Complectens Nunc Bibliothecam Perfectam Viri Ecclesiastici, Ordine Sequenti, (Antwerp, 1678), Octavo.