He reformed Aquinas' third way (that there must be a necessary being outside the universe who caused it, but is themselves uncaused - the uncaused causer and unmoved mover), saying that the first cause must have necessary existence.
He believed in a hierarchy of causes, with God at the top of this.
He said that the universe is made up of contingent things, so must be contingent.
He argued for a God unlike that of Aristotle's Prime Mover, who caused everything then had no interaction with the universe.
He said to Russell during the debate, "If one refuses to sit down and make a move, you cannot be checkmated".
He opposed Copleston in the debate, and questioned why people thought the universe needed to have a first cause - "I should say that the universe is just there, and that is all". He said that its existence is a "brute fact".
He argues that the concept of a 'necessary being' had no meaning for him as the term 'necessary' cannot be applied to things, only to logical statements where B necessarily follows from A as it part of the definition (for example if someone is a bachelor, they are necessarily an unmarried man as that is the definition of a bachelor).
Copleston was trying to make sense of the universe, but Russell argued that this was pointless and that the universe did not have to make sense.
In response to Copleston's chess analogy, he said that it was "skewed towards the theist" as in order to engage with Copleston, he would have to work within his logic, which Russell denied.
By the end of the debate, Russell and Copleston concluded that they had very little ground in common.
They could not even agree on whether they were discussing a question which had any meaning, so they decided to leave the issue and move onto another.