Logic question about the sum of one's free choices

If each moral choice a person makes is free (as in free will) it seems to follow that the sum or totality of all those choices is also free. In other words, if each individual sin can be avoided, then sinning in its entirety can be avoided. I thought maybe there was an abstract way to represent necessity in the sum of all choices implying necessity in at least one of the particular choices.

• Even if each choice is free it does not follow that taking any of the available options avoids sinning. And which options are available depends on choices previously made, as well as (and, perhaps, primarily) on choices made by others and random chance. So I do not think that this individualization of necessity is going to work. Indeed, there is a well known argument of Plantinga showing that even an omniscient and omnipotent God can not prevent free creatures from sinning without subverting their free will. – Conifold Aug 29 '20 at 20:30
• @Conifold The argument assumes each individual sin can be avoided. I realize there could be different definitions of sin that would change that. I'm looking for a way to represent the contingency/necessity of the parts and the whole with symbolic logic or something like that. Is there any way to do that? – Benjamin Stenson Aug 29 '20 at 20:59
• It is not the definition of sin that prevents it, in Plantinga it is the metaphysics of free will that does, regardless of what counts as sin. I am not sure what you are trying to do, but perhaps you could use the necessity operator of modal logic to do it. Something like □(∃xS(x)) → ∃x□S(x), if one necessarily sins somewhere then there is some necessarily sinful choice? Again, I do not think this works, some choices are only sinful in concert with other choices, not on their own. It is only sinful to promise when it's a lie. – Conifold Aug 29 '20 at 23:57
• @Conifold Modal logic looks like it's probably what I'm looking for. Thank you. Say you get 100 choices in life and your first 99 choices were not sinful. If it's impossible to go through life without making a sinful choice, then your 100th choice will necessarily be sinful. Does that make more sense? I'm critiquing a simple claim that we're able to avoid each particular sinful choice yet can't make it through life without making a sinful choice. – Benjamin Stenson Aug 30 '20 at 3:22
• Say your first 99 choices led to you having to choose between stealing and having your family starve to death. You are not fully responsible for the dilemma, as it is brought about also by choices of others. Which of the choices then is necessarily sinful? It is not the 100th, as it could have been avoided by different earlier ones, but alternative choices could not guarantee avoiding this or some other dilemma either, as it is unknown in advance what they lead to. The problem is that life is not a sequence of independent trials with complete information. – Conifold Aug 30 '20 at 20:25