The advantage of truth tables is that they deal with double negatives.
What the chart above in plain English is that:
It’s true that it’s true
It’s true that it’s false
It’s false that it’s true
It’s false that it’s false.
The two that equal each other as being true are it’s true that it’s true and it’s false that it’s false.
In debates, ambiguity occurs with the middle two of the truth table: it’s true that it’s false and it’s false that it’s true both solve as “false”, and also as a paradox, to make debate subjects unnecessarily confusing.
It helps to point out which of the four truth tables is being utilized to clarify where parties are at with respect to presenting their subjects of debate.
To have a grid that’s more than true : false and the two gridded truth tables becomes redundant. It’s only important to this regard to discuss what is commonly known as the truth table which allows for double negatives and more.
The latter all mean: not necessarily true and/or false.
This solves as a contradiction to the reason for stating it in the first place, unless it has a qualifier as to WHY!!, which puts it back on the truth table.
Empirical truth is on a spectrum so it cannot be limited to just four variables
Those four varaiables may be false anyway where such truth is concerned because of the problem of induction
For example something may be regarded as true because of evidence but subsequent evidence may falsify this
Only where proof is concerned with regard to logic can one deal in absolutes
So for example the statement one and one is two is absolutely true because it can never be falsified
Because mathematics is a branch of logic and logic uses proof to determine the truth of propositions
That’s not true. The truth value of a representation can be binary classified and that’s usually enough. But not always, of course. Sometimes, you want to know the degree of falsity i.e. how false a belief is. If you’re 6’3’’ and I think you’re 6’4’’ then I am wrong but not as wrong as I would’ve been if I thought you’re 5’8’'. And if it was necessary to know how wrong I am, then simply saying I am wrong, although true, wouldn’t have been enough.
You can look at it another way.
The statement “1 + 1 = 2” is a statement about language. What it means is “Everything that can be represented by expression 1 + 1 can also be represented by number 2.” This is either true or false and it depends on the rules of the language of our interest. Since the rules of any language can be observed, e.g. in the way it is being used in practice, the statement is not so different from the so-called empirical statements. Even if it’s a language you invented just a few moments ago, you must recall the rules you’ve invented; the choice is certainly not an arbitrary one. In other words, the statement can be falsified.
Every statement that has truth value (which is to say, every statement that is a representation of some portion of reality) is testable and therefore falsifiable (since tests either verify or falsify a claim.)
Ec, baby. That’s not how you read those truth tables. That’s the chart for two terms to which a logical operator will be applied. You use this chart to account for all truth value (T or F) combinations of p and q and then you add a column for the expression that you are using these two terms in, to find out what happens in each case. It’s got nothing to do with a “double negative” per se.
You can make a truth table with double negative truth values, but I have no idea why you’d want to that.
Your “plain english” translations are probably worth copywrighting, as they are yours alone, so far as I know.
That makes no sense. Truth tables really exist, they are used to deconstruct paradoxes.
It makes no sense to say “true or true” “false or false”
But that’s exactly what a truth table is!! T/t, t/f, f/t, f/f. The whole point of a truth table would be meaningless if they all just used the “or” operator
Lots of natural language problems use double negatives. It’s true that it’s true solves as identity.
I looked it up. You are correct by the books. I’m going to use my ideosyncratic representation of truth tables for my own purposes.
To me, the regress (which can’t go any further than 2 variables without being redundant) is very useful. Regress is very useful in argument. You can’t get regress with t or f.