Bitcoin transactions are a process of renaming a coin according to the rules of the protocol, yet agreed upon as a consensus.
The function of naming itself can be played in two levels:
One is the individual level in which I can name things to organize it in my own mind. Each of us is free to name anything they want in which ever way they wish at that level. however we cant communicate with each other based on these individualy made name
The other function of naming is to allow communication between different individuals. This function involve another party, that of the other one. Thus is means that a naming is in fact an agreement, a sort of a contract between two or more individuals.
In fact the most fundamental contracts between individual are the names. Logic is the rules by which the connection between the named ones is formed. However to form the rule one need to agree on some names first. These first name are the axioms.
Bitcoin transactions are a process of renaming a coin according to the rules of the protocol, yet agreed upon as a consensus.
The protocol alone can not decide and is not design to decide which is the right name out of conflicting two different names to the same coin's original name (hush name + wallet address) is the right name. The fact that the wallet address is part of the coin's name made this coin resilient to dabble spend. The consensus thus is not about the truth as right or wrong,. it is all about the naming.
In order to keep agreeing on the most basic sentence , A go to B (a transaction), we agree on what is B based on A. We let A name B.
However if "A" (Alice) gives two names for "B" B.1 and B.2 (BOB and Bill) we agree that B is what most nodes decide on, whether its B.1 or B.2 dose not matter. The nodes and our collective truth dose not care whether it is Bob who will get the coin or Bill. Our collective blockchain based truth don't ask or bother with justice!