# 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.).

## 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.