Whatever happens within the system is not only possible, it must necessarily happen.
Correct, but you have yet to acknowledge the possibilities that must necessarily not happen.
If events come to the point where you feel the need to 'add a column of numbers' for whatever reason drives your need, you add your column of numbers as determined.
Correct. And, it is indeed my own reasoning that motivates and directs the behavior.
By your own definition, there are no alternatives, you add your column of numbers and you do it without impediments because - if determined - it is a necessary action.
If it is causally necessary that I will add a column of numbers, then I certainly will do so. But we cannot rule out alternatives or impediments. There actually may be alternatives, but I will not choose them. There actually may be impediments, but I will overcome them.
Causal necessity does not eliminate alternatives or impediments. Any alternatives or impediments that show up will also be causally necessary from any prior point in time.
With causal necessity, there will be no alternative to the events that actually occur, including the events in which we encounter alternatives and the events in which we encounter impediments.
You may find the two uses of "alternative" confusing. But in one case we are speaking of the overall series of events, and in the other case we are looking
inside specific events, such as choosing, which logically require the multiple alternatives to operate. Choosing always requires two or more alternatives to select from, just like addition requires two or more numbers to sum.
In a deterministic system, it is still possible for someone to be free to choose what they will order from the restaurant menu.
There are no alternatives to choose from. Which, again, is not to say that any number of alternatives do not present themselves to us as we go about our business.
If it "is not to say that any number of alternatives do not present themselves to us as we go about our business", then one cannot say that "there are no alternatives to choose from". Either the alternatives are there or they are not there. We cannot look at the restaurant menu and say that the alternatives are not there. A menu is literally a list of alternatives to choose from.
The point being, that however many apparent alternatives there are, the decision we make in any given instance is the only possible action for us in that moment in time.
An alternative is a possible action. When faced with the restaurant menu, we cannot say that there is only one possible action.
An alternative need not be selected in order to qualify as a possible action. The fact that an alternative will not be selected does not make it "impossible" to select, but only "not selected".
That is how determinism is defined, and it is a condition of your own definition of determinism.
No, sir. It is not a condition of my definition of determinism. Determinism is the reasonable belief that all events are reliably caused by prior events, such that every event is always causally necessary from any prior point in time. This includes the physical events, such as motion of the planets, as well as the mental events happening within our own brains (which correlate to neurological processes).
When we encounter situations where we must make a choice before we can proceed, it will always involve two or more possible actions. These choosing events, such as ordering dinner in a restaurant, will proceed deterministically with no deviation. It will be true that two or more actions will be possible and it will be true that we can select any of the alternate actions. These will be true by logical necessity, just as it is true that a triangle has three sides.
... As it is defined, there being no deviation as the system unfolds, progresses, evolves or develops, there are no possible alternate actions.
Apparently that is not the case. There will be no alternative to us encountering alternatives that we must choose between. That is how the system unfolds, progresses, evolves, develops deterministically. We will encounter alternatives, which causally necessitates that we must choose between them.
'Must' overrides 'will' and 'can.'
Apparently not. Deterministic causal necessity insures that we must encounter that menu of items we can order in the restaurant, and that we must choose what we will order for dinner from among those alternate possibilities.
There is no way to get to the single thing that we will order without first dealing with the many things that we can order.
Confusing what we can do with what we will do creates a paradox. We cannot "choose between a single possibility". Multiple options are required, and, there they are, listed on the restaurant menu. We are able to choose any one of them, even though it is causally necessary that we will choose only one.
The notion of possibilities evolved to deal with our uncertainty as to what will happen. When we do not know for certain what will happen, we imagine what can happen, to prepare ourselves for what does happen
The notion of possibilities also serves us by providing a logical workspace for invention, creativity, and progress.
Equating what can happen to what will happen destroys the notion of possibilities, the logical operations that depend upon them, and the survival advantage that we humans possess by having an intelligent brain.
So, let's stop making that error of equating what can happen to what will happen and what does happen. An evolved human mind is a terrible thing to waste through illogical thinking.
The notion of possibilities is an expression of the limited perspective of our position within the system. We lack the necessary information to make accurate predictions in relation to complex events. There are just too many elements at work that we have no access to.
Indeed. If we had omniscience, then we could dispense with the notion of possibilities, because we would always know in advance what would happen next. But omniscience is clearly not the case. So, we should understand and correctly apply the notion of possibilities if we wish to deal effectively with our real situation in the real world.