This answer will vary, primarily because definitions of the concept of justice will vary. In my mind, the definition of justice has to be something permanent, something that represents the transcendent in a world of contingency. It is for this reason that Proctor's closing speech is what best represents the theme of justice in my mind. Consider his closing words when he is forced to sign his "confession:"
Because it is my name! Because I cannot have another in my life! Because I lie and sign myself to lies! Because I am not worth the dust on the feet of them that hang! How may I live without my name? I have given you my soul, leave me my name!
The idea of Proctor's "name" is what is transcendent to him. It is this idea that motivates him into action because he recognizes how the embrace of the contingent is not necessarily a pursuit for justice. Proctor recognizes this in his last moments of life, and to this end, he commits himself to the idea of embracing that which is transcendent and universal. The defense of one's name and one's reputation has to move one closer to the idea of justice because it subjugates the individual to something larger than oneself, precisely embracing the aim of justice.
It is for this reason that Proctor's speech represents justice and why Abigail does not. Proctor's speech provides a great pivot towards why Abigail cannot represent that which is just, for Abigail acts only in her own interests and never in that of the community. In starting the rumors and accusations of witchcraft, she seeks to advance her own agenda and purpose. In embezzling money from Parris and running away, she continues to serve her own interests and nothing in the name of justice and honor. For Proctor, being able to fully represent that which is transcendent and away from that which is contingent is that which is justice. In seeking to embody this, Proctor's closing quote is what represents a definition and vision of justice, a symbol for all to emulate and one that ends up providing hope and redemption in a setting that is devoid of it.