Objection 1. It would seem that a second marriage is unlawful. Because we should judge of things according to truth. Now Chrysostom [Hom. xxxii in the Opus Imperfectum falsely ascribed to St. John Chrysostom] says that "to take a second husband is in truth fornication," which is unlawful. Therefore neither is a second marriage lawful.
Objection 2. Further, whatever is not good is unlawful. Now Ambrose [On 1 Corinthians 7:40 and De Viduis] says that a second marriage is not good. Therefore it is unlawful.
Objection 3. Further, no one should be debarred from being present at such things as are becoming and lawful. Yet priests are debarred from being present at second marriages, as stated in the text (Sent. iv, D, 42). Therefore they are unlawful.
Objection 4. Further, no one incurs a penalty save for sin. Now a person incurs the penalty of irregularity on account of being married twice. Therefore a second marriage is unlawful.
On the contrary, We read of Abraham having contracted a second marriage (Genesis 25:1).
Further, the Apostle says (1 Timothy 5:14): "I will... that the younger," namely widows, "should marry, bear children." Therefore second marriages are lawful.
I answer that, The marriage tie lasts only until death (Romans 7:2), wherefore at the death of either spouse the marriage tie ceases: and consequently when one dies the other is not hindered from marrying a second time on account of the previous marriage. Therefore not only second marriages are lawful, but even third and so on.
Reply to Objection 1. Chrysostom is speaking in reference to the cause which is wont at times to incite a person to a second marriage, namely concupiscence which incites also to fornication.
Reply to Objection 2. A second marriage is stated not to be good, not that it is unlawful, but because it lacks the honor of the signification which is in a first marriage, where one husband has one wife, as in the case of Christ and the Church.
Reply to Objection 3. Men who are consecrated to Divine things are debarred not only from unlawful things, but even from things which have any appearance of turpitude; and consequently they are debarred from second marriages, which lack the decorum which was in a first marriage.
Reply to Objection 4. Irregularity is not always incurred on account of a sin, and may be incurred through a defect in a sacrament ["Defectus sacramenti," i.e. defect of signification; Cf. 2, Objection 3]. Hence the argument is not to the point.
Source: Summa Theologica (New Advent)