How do we ground ontological identity?

What is identity? Why and how do we assign and believe objects to be identical and identifiable? And this question is very difficult for mathematical "structures" which are identified in a a creative way: let X be such-and-such a structure and let a be an element of X.  How do we even identify and constitute ontological continuity for a symbol or a name? Why is "a" at one point of the page the same "a" at a different point? And why is its semantic and intentional aspect exactly the same? And when we say: let X be such-and-such a structure, exactly how do we point out (or create or bring out through ekthesis) this structure for a given context? Numbers, algorithms, structures - what gives them their abstract identity and identifiability? How are they named and pointed out and discussed? How do they subsist in the human mind and memory? How are they recalled and are they the same each time they are recalled? Does the human mind ever really act like the common notion of a rule-following algorithmic process? How can this be if we cannot identify the whole or the parts and do not know what guarantees their consistency or continuity? What really was so-called psychologism and was it really "refuted"? Does the very notion of "refutation" in this context even make sense? Can we point to a "structure" on a computer? The bare physical configuration of the hardware. It is we who "interpret" it.  But it does not really exist in a certain sense. Ethical perception can never be directed at an abstract "structure" but only at life. The machine is the counterfeiting of life, turning life into "structure".  The soul instead of seeing herself as an anagogic image became a stranger to herself and instead worships structure and the machine. Language is an aspect of mind which is in constant danger of being misperceived as an allegedly stable abstract structure when it is not. When the word arises the thought and meaning process has already ceased. All structure is the product of individual and social consciousness and can only be understood in terms of it.