The Binary Circumstance links to Objectivism and the Primacy of Existence.
When Ayn Rand distinguishes ‘existence’ from ‘consciousness’, she mainly means by “existence” what other philosophers call “the external world” — thus, the distinction is between states of one’s own mind and external phenomena. According to Objectivism, existence has primacy over consciousness in two senses. First, epistemologically: human knowledge begins with (sensory) awareness of the external world. It does not begin with awareness of one’s own ideas. The reason is that ideas or states of consciousness are necessarily ideas about something, and that something is what one is aware of. One could not become aware of one’s own consciousness, unless one first had some states of consciousness to be aware of; and one could not have states of consciousness, unless one first had something else that one was conscious of.
Something I like to bring up is that even though the Forms exist independently of any observer, and thus existence is “prime” over consciousness, that doesn’t mean that everything your senses tell you is true. The world we create in our minds is based upon the physical experience of the real world, but it is not the same world.
Example: A blind person who has always been blind does not have the concept of colour in their mind world. Does that mean it doesn’t exist? No. Given the assumption that both time and space are infinite, or beyond human contemplation, then we cannot be completely sure that sometimes does NOT exist (like colour) nor could we tell if it didn’t. Thus, there is no absolute and completely understanding of reality–often called Truth.
There are only the various truths that we decide on as a culture and our primary tools to create these truths are reason and experience.