wiki:FirstPrinciples/Logic

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 Falses), 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.

Last modified 15 months ago Last modified on Nov 23, 2018, 12:43:37 PM
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