Formalisation

Both of the following contexts are from the same chapter of a same book. I think the yellow "formalize" means "to give form to", while the green "formalize"s in the second context imply "to define". Am I right?

Context #1:

The ethics involved here is that the excess of destructiveness that seems to be inherent in human sexuality is dissipated via an internal relation to a surrogate self rather than projected outwards and inflicted on an external object in the exercise of ‘mastery or the will to power’. The formalisation of destruction in the art encounter allows us to repeat the painful pleasures of what theorist Leo Bersani calls an ‘ecstatically shattered ego’, which is a repetition of the originary ‘threat of stability and integrity of the self that human sexuality is’.

Context #2:

But it was Freud who formalised the notion of the unconscious as a psychic mechanism whose workings were made apparent in dreams, slips of the tongue and forgetting. These operations are considered irrational from the perspective of objective reason, but Freud showed that they had their own logic bound up with the expression of repressed wishes and desires. In formalising the unconscious in this way, Freud severed its links to Romantic inspiration and brought this area of psychic functioning into the realm of everyday behaviour.