# Proper Logic

Asymmetry of truth and falsehoods. These are not necessary exact opposites. (intuitionistic logic)

Everything that does not exist (is not) is `False`

not True = False

Whatever *cannot be falsified* (this and only this) is `True`

or *just Is*

not False = True

## Logical connectives

`IMPLICATION`

or `->`

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

Universal quantifier `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.

## Functions

One more time

At least one `Truth`

(discards `False`

s), if ALL `False`

, then the whole is `False`

.

(||) False x = x

or just *no need to look further* beyond the `Truth`

(short circuiting)

(||) True _ = True

Obviously, `False || False`

is never `True`

a single `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

## Implication

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

Implication from `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.

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