Copyright Carl Janssen 2024 September 7
Vacuous Truth or Vacuous Falsehood
Let's say two days ago, or in other words the day before yesterday, Rob said, "if I do P tomorrow then Q will happen tomorrow"
Now today Samantha says, "Q never occurred yesterday so Rob was lying"
In reply Alexander says, "A statement can only exclusively either be one of two options of true or false but not both and there is no third possibility. P did not happen yesterday so Rob's statement is not false so that only leaves one other option and this makes Rob's statement vacuously true. All statements with counterfactual antecedents also called true protasis have true consequents also called true apodosis"
Samantha replies that if Rob said, "if I do P tomorrow then Q will not happen tomorrow would that also have been vacuously true"
Alexander replied, "yes"
Then Samantha said, "then since we know that Rob said if I do P tomorrow then Q will happen tomorrow but we know that it is vacuously true that Q would not have happened tomorrow, this proves that Rob's statement that Q would have happen tomorrow vacuously false because if it is true that Q did not happen that day then it would be false that Q did happen that day"
Alexander replied, "P did not happen yesterday so there is no evidence that Rob's statement is false and if there is no evidence that it is false then it must be true"
Samantha replied, "The only way for there to be evidence that Rob's statement was true would be if P did happen yesterday and Q also additionally happened yesterday and since there is no evidence that Rob's statement is true then it must be false."
Alexander replied, "Now you got me all confused Samantha. The statement can only be true or false and only one of those two options and those are the two options. But a compelling case can be made that it is true and also a compelling case can be made that it is false."
Samantha replied, "Although you are correct that a statement can not be both true and false simultaneously when measured in the same way, the reason for your confusion is because there are more than two options. You can not know if Rob's statement is true or false because since the claim that P happened yesterday never occurred Robs statement is untested we could try to guess at whether or not Q would have happened if P happened and guess whether the statement would be true or false on that basis but since P never happened his statement would be better described as untested then confirmed to be true or false. Always using the type of logic that limits things to two options of only true or false really does not line up well with the scientific method because some things although they might in reality be only true or false are untested so we should just label them as untested and make the claim that we do not know they are true or false instead of insisting on assigning them a value of being true or false when we do not know which of those two values is correct. Also depending on how you look at things maybe there could be other options then true or false. It is important to keep in mind that being proven true is not the same as being true and being proven false is not the same as being false. Something can not be both true and correctly proven false if you are measuring with a single consistent standard but something can be both true and not proven true at the same time. Likewise something can not be both false and correctly proven true if you are measuring with a single consistent standard but something can be both false and not proven false at the same time. One might argue that under a certain standard there could be two potential values of one kind for a certain statement of either true or false but simultaneously three potential values of another kind of either proven true, untested or proven false. If something is not proven true then it could be true, untested, proven false or false but it could not be proven true. If something is not proven false then it could be false, untested, proven true, or true but it could not be proven false. If something is correctly proven true then it could only be true. If something is correctly proven false then it could only be false. If something is true then it could only be true, proven true, untested but it could not be false nor correctly proven false. If something is false then it could only be false, proven false or untested but it could not be true nor correctly proven true. If something is untested then it could be true or false but could not be proven true nor proven false. Now in this standard if something is proven true then it is both true and proven true. Also in this standard if something is proven false then it is both false and proven false. This is only one standard of looking at things under another standard there could be more nuanced options then true and false, under such a standard something could not be both simultaneously true and not true but being not true would not always mean it is false because there could be a third option. Likewise something could not be both simultaneously false and not false but being not false would not always mean it is true because there could be a third option. It is also important to keep in mind that depending on the view point saying that some object S is not not K is not necessarily the same as saying the object S is object K although it could be the same depending on another view point but maybe one of those two view points might be wrong, but maybe both viewpoints or even additional viewpoints could potentially be right depending on the circumstances. One of these viewpoints is that if an object S is not not the object K then the object S is the same as the object K, I will not go into detail further on this viewpoint because it is a standard viewpoint. Now for an unorthodox viewpoint. Let's say there is a computer programming function where you select a input from a list of three words, spoon, fork or knife and it gives you an output that is one of those three words but is not the word you select. So if you select spoon you will get an object that is not a spoon such as a fork or a knife. But if you run the function a second time with the output that you got from the first time you run it you could end up with a spoon again but you could also end up with a fork or a knife as long as it is not the same object as the output that you got the first time you ran the function. You could say that the function negates your choice, so running it twice is negating your choice then negating it again but you would not necessarily end up with the same choice that you started with even though it is claimed that double negating something ends up where you started. Perhaps double negating only guarantees consistently ending up where you started if you negate something by selecting a list of every object that is not on your list and not having a single object that is on your list each time when you negate the list. To be more technical we could talk about every item in a sample space vs every item even items we are not working with and still have it work so long as we never list items outside the sample space when negating and stick with the same sample space to select from neither adding from it or subtracting from it in all operations although I am not sure this is worded correctly because the language is a bit too technical in definitions for me at this point. I also want to point out that double negating only consistently works this way where you end up with what you originally had if you negate it twice in English when each of the two words that say 'not' are right next to each other with no words in between in a sentence. For example to say let's assume if something is a dog it is an animal is a statement that is always true but to say if something is not a dog it is not an animal is a statement that is not always true even though two negations were added two the sentence, however to say that if something is not not a dog then it is an animal would be a statement that would be always true based on a certain viewpoint because the two times the word "not" is used each 'not' is next to the other 'not' with no words in between"
Alexander replied, "But how do you apply this"
Samantha replied, "If P happens then Q will happen on the same day has been claimed. Since P did not happen it has not been confirmed or proven false that Q will happen if P happens but just because it was not proven false does not mean that it is proven true. Since P did not happen it also has not been confirmed or proven true that Q will happen if P happens. The statement could be true and the statement could be false but the statement could not be both true and false, the statement is untested and neither proven true nor proven false. It is important not to confuse true with proven true nor to confuse false with proven false. It is important to remember that not false does not necessarily mean the same thing as true nor does not true necessarily mean the same thing as false depending on what logic system you are using. And finally depending on how you try to negate something twice it does not necessarily result in ending up where you would have started with zero negations if that also somehow is related to this confusion although I am not sure if it is. If there is a list of three or more options when someone thinks there is a list of only two or more options they might choose something that is not object 1 and assume it is object 2 then choose something that is not object 2 as a second negation and assume they are going back to object 1 and undoing the second negation when they could actually lead to object 3 by choosing something that is not that object a second time. For example if someone says choose something that is not a spoon and they select a knife and then they say now choose something that is not the thing you just selected and they think the only option is a spoon when it could actually mean a fork."
https://en.wikipedia.org/wiki/Consequent
https://en.wikipedia.org/wiki/Antecedent_(logic)
https://en.wikipedia.org/wiki/Paradoxes_of_material_implication
https://en.wikipedia.org/wiki/Principle_of_explosion
https://en.wikipedia.org/wiki/Double_negation
https://en.wikipedia.org/wiki/Law_of_excluded_middle
https://en.wikipedia.org/wiki/Counterfactual_conditional
https://en.wikipedia.org/wiki/Vacuous_truth
https://en.wikipedia.org/wiki/Three-valued_logic
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