Unassailable dichotomies?

[sprinkles]

alright, so. The vault being open or not is that a dichotomy? not the variable.

In the sense of very abstract ideal states in complete isolation, yes it's a dichotomy. However this is like assuming instant acceleration when calculating a required change in velocity - it makes things neat but only in the theoretical realm. When it comes time to apply that change in velocity to a real vehicle you quickly discover that you in fact cannot accelerate instantly.

 

[Elis]

[MENTION=6917]sprinkles[/MENTION]

So we have a definition where the vaults state (not the variable) is a dichotomy.

let's say we run a program. When it executes, the first thing it does is to check the state of the vault and assign it to (state).

state := (actual vault state)

now we apply the loop

if(current_level >= max_level):
   state := true
if(current_level <= minimum_level):
   state := false

Now there will not be any invalid state. How is this not a dichotomy?

(state) and ¬(state)

 

[sprinkles]

So we have a definition where the vaults state (not the variable) is a dichotomy.

let's say we run a program. When it executes, the first thing it does is to check the state of the vault and assign it to (state).

state := (actual vault state)

now we apply the loop

if(current_level >= max_level):
   state := true
if(current_level <= minimum_level):
   state := false

Now there will not be any invalid state. How is this not a dichotomy?

It depends on conditions which are not binary in nature.

Moreover, due to the way the expressions are written there are many ways that each one can evaluate as true. For example if max_level is 100 and current_level can be more than 100, then the pump will turn on at not just 100, but also 103, or 107, or 112 etc. so basically you have different "flavors" of being true here. This could actually be relevant if you need to track something about the performance of the system.

 

[Elis]

[MENTION=6917]sprinkles[/MENTION]

Well, of course. But the expression would still be a dichotomy, would it not?

 

[sprinkles]

[MENTION=4361]Elis[/MENTION]
Or basically if the pump turns on at 101, this may have a different practical significance than if it turns on at 105. So while the state is the same the implications can be different. If it's only responding at 105 and not 101 then it may not be computing quickly enough, or the pump is not responding quickly enough.

In other words different flavors of truth could be used for diagnostics. That's just one example. Since they're not only identifiably different but also usefully different, I would say this is not a dichotomy because it breaks the definition of exclusivity.

 

[Elis]

[MENTION=6917]sprinkles[/MENTION]

I don't see how that would invalidate the dichotomy. (105>=100) is not more true than (101>=100).

 

[sprinkles]

[MENTION=6917]sprinkles[/MENTION]

I don't see how that would invalidate the dichotomy. (105>=100) is not more true than (101>=100).

It is a noticeably different kind of true. The fact that it is a different option is what matters and is what invalidates the dichotomy. A dichotomy cannot have non exclusive evaluations.

 

[Elis]

[MENTION=6917]sprinkles[/MENTION]

It isn't exclusive, (101=>100) and (105=>100) are both defined cases. there is no such thing as different kind of true in Boolean expressions.

 

[sprinkles]

[MENTION=6917]sprinkles[/MENTION]

It isn't exclusive, (101=>100) and (105=>100) are both defined cases. there is no such thing as different kind of true in Boolean expressions.

This is reaching to keep it a dichotomy beyond any practical purposes. One can come up with very good reasons why this is not a dichotomy in the real world. I already did actually.

In fact I'd argue that if it's not a dichotomy in the real world then it isn't one at all, because the real world is actual and Boolean logic is a constructed subset.

 

[Elis]

[MENTION=6917]sprinkles[/MENTION]

I give you that. but let's separate the variable from the reality. The variable is either true or not true. Regardless of how it represents reality, it is a dichotomy. No?

edit: then again, you could always point to computer malfunction. I guess I only see it in the theoretical plane.

I need to catch some sleep. It was fun talking though

 

[sprinkles]

[MENTION=6917]sprinkles[/MENTION]

I give you that. but let's separate the variable from the reality. The variable is either true or not true. Regardless of how it represents reality, it is a dichotomy. No?

edit: then again, you could always point to computer malfunction. I guess I only see it in the theoretical plane.

I need to catch some sleep. It was fun talking though

Well in regards to the state it can either be completely on or completely off so in that regard there is a dichotomy. Switches are often designed this way to avoid excessive arcing by minimizing the travel time of the contacts. I already acknowledged this though.