Entering true or false as text into any cell is interpreted as TRUE or FALSE

=SUMPRODUCT({TRUE};1) 

Result is 1 in Calc and 0 in Excel.

You had been given some examples and an explanation. The industry standard in the field of spreadsheets is use of these two words as keywords for boolean values. The industry standard is also to try to convert everything that user enters as a source for either number or formula (by default). The opinion of logophiles is indeed valuable, but in some other contexts. Thank you for the interesting abstract discussion.

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If you reveal all the sigma functions and just type their name without parameters in any cell it’s just treated as text and I will assume it’s the same for all CALC functions. If you type true or false it becomes a function without any parameters.
What I don’t understand is how these parameterless functions can be useful in isolated cells.
You did indeed provide some examples but they presumably utilised TRUE or FALSE within their cell formulae and not requiring references to external cells simply loaded with TRUE or FALSE.
Are you implying you write a formula calling either TRUE or FALSE according to some test -in that formula - from an external cell identified by that test and then use the TRUE or FALSE logic on parameters contained within that formula (or external calls)?
It may be industry standard but I once worked in a company who imported a CEO from outside and he called us all together and explained how we were all going to adopt a new procedure. When I asked him why he replied “Because we used to do it at Hewlett Packard”. I responded “It doesn’t matter where you may once have performed that task, what I’m asking is how does that benefit us or our customers”. He didn’t know the answer - and was replaced about 6 weeks later.

In Calc, boolean values are just number formats for zero and non-zero.
and if they are simply present in a cell with no parameters then there is something in each of those cells that is of numeric or non numeric value - so doesn’t that imply they are both true

It’s using wrong tool for the job. It’s your task to check if Calc fits to you (or your customers). But it’s not like “it doesn’t matter what Calc did before”, because it indeed does for millions of users; and if you can’t live with that, you will leave (this site) 6 weeks later.

Not everything that Calc does is to benefit you personally. You persist in claiming that if you can’t see the benefit, there’s none (for anyone else). It’s not a correct approach, and you don’t face your employees here, who are obliged to clarify it ad nauseam.

Do these words have the same sense in English as Yes and No, On and Off, Open and Closed? Truth and Untruth? Or do logophiles not know synonyms to replace reserved words?

I think you misunderstood the analogy. I’m looking for an explanation of how a parameterless function is utilised. I don’t understand how looking at a cell that says true or false is incorporated into a formula any better than an if;then;else You gave an example of when you might use it but no sample of the structure or how it works. It was much better than “we used to do it…” but unfortunately provided little insight into how that remote cell containing true or false is generated or selected. Is it more adaptable/accurate/efficient than IF x do y else do z? Telling me that everybody does it because it’s there is not the same as explaining what the benefits are to somebody who only ever encounters the TRUE/FALSE scenario when using functions like VLOOKUP() and defining whether the requirement is for an exact or a fuzzy match. The validity is assessed by the calling function defined by the users’ parameters within that function, not reference to range A1:A2 containing TRUE or FALSE - now lookup using A1 or A2.

I said explicitly: that was one of the constants. I.e., a user simply types “true” there. You just expect every such cell to be generated by an automation; no it is not. Today I want to count with this set; I type this value, and see the result. I type another, and have another set of results. It’s a kind of manual “what if”. And that was just a simple example that came to my mind.

So its interrogative - I might say “what month do you desire” and the answer is Sep or 9 and you would say “Do you want Sep” and the response is TRUE

I suggest returning to the starting question.
When you enter a value into a cell, the spreadsheet program (Calc, Excel) tries to “guess” your intent and minimize your effort.
Which of the 2 options that have the same result in Calc is more convenient for the user entering data into a cell of a general format?

  1. Enter a value 1. Open the cell format dialog and select the “Boolean Value” format.
  2. Enter true.
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Good idea.
I’m now beginning to understand and I think it depends upon the experience of the person entering the data.
I have previously used mechanisms where I just expect any character entered into the “check-box” with the test if(A1="";action1;action2) and I now understand I can just use If(A1;action1;action2).
I feel expecting “true” or “false” is a little “long-winded” and that letting the mere presence of data in the cell be the trigger for further action is perhaps “friendlier”.
My approach has been successful until I just happened to search for the word “False” in an array of 7000 entries which kept disappearing - it was never going to find 0 so both the trigger and target were seemingly (impossibly) null. Good old IFERROR() prevented anything remotely resembling a warning.
It transpires that my cell fill was exactly the same colour as the auto colour when Calc chooses to represent text and results in two predefined colours - setting FALSE to result format instead of text.
The original data was imported as a text file and happened to be placed into text formatted cells.
The enquiry was written on a different sheet which had the Calc default cell format.