Asymmetry of truth and falsehoods. These are not necessary exact opposites. (intuitionistic logic)
Everything that does not exist (is not) is
not True = False
Whatever cannot be falsified (this and only this) is
True or just Is
not False = True
-> means a transition, a proven fact, a valid step, based on previously proven facts
WHEN this THEN that.
I is not
IF THEN ELSE - there is no predicate to check, there is no question and there is no ELSE. Implication is not a conditional expression, its conclusion is a statement of fact. It is universally valid - it IS.
Valid (proven) implication could be substituted with its conclusion (statement of fact). The whole chain of nested proofs, all the way from (traced back to) the the first premises (or axioms) could be substituted with the last conclusion.
AND means simultaneous, together, more than one (attribute, property, slot)
AND means a compound,
this AND that
A single falsehood is ruins the whole chain or a sequence of thought (of anything!)
(&&) False _ = False (&&) True x = x
OR means alternative, choice, different outcomes, configurations.
OR means partitioning,
this OR that
This partially applied Truth - the basis for short circuiting
(||) True _ = True (||) False x = x
FORALL distributes over
AND - when one element of the domain has
this AND that properties then
ALL elements of this domain has
this AND that properties. This is called universal generalization (for categories - Socrates, is a man, etc.).
Similarly multiplication distributes over addition.
One more time
At least one
Falses), if ALL
False, then the whole is
(||) False x = x
or just no need to look further beyond the
Truth (short circuiting)
(||) True _ = True
False || False is never
False falsifies the whole
(&&) True x = x
or just no need to look further beyond
False (short circuiting)
(&&) False _ = False
So, a valid antecedent - *all* premises are True
every = foldr (&&) True
Here comes bullshit
A partial function for Natural Implication - when all premises are True,
and implication itself is True, then (and only then)
x is True.
(==>) :: Bool -> Bool -> Bool True ==> x = x
This is an utter bullshit of abstract nonsense
False ==> x = True
False has no equivalent in the real world in the same way addition of 0 and multiplication by 1 have no corresponding processes in What Is. Universe never adds 0 or multiplies by 1.
These are perfectly valid abstract operation and in cases of
a + 0 = a and
a * 1 = a are perfectly
True propositions, but they never happen in reality. The same is true for False implies anything. It never happens.
So, every logical formula (proposition) which includes an implication from
False is bullshit.