Logic
Logic (from the Ancient Greek: λογική, logike) is the branch of philosophy concerned with the use and study of valid reasoning. The study of logic also features prominently in mathematics and computer science.
Logic was studied in several ancient civilizations, including Greece, India, and China. In the West, logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. In the East, logic was developed by Hindus, Buddhists and Jains.
Logic is often divided into three parts: inductive reasoning, abductive reasoning, and deductive reasoning.
The study of logic
The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.
Ω-logic
In set theory, Ω-logic is an infinitary logic and deductive system proposed by W. Hugh Woodin (1999) as part of an attempt to generalize the theory of determinacy of pointclasses to cover the structure 
. Just as the axiom of projective determinacy yields a canonical theory of 
, he sought to find axioms that would give a canonical theory for the larger structure. The theory he developed involves a controversial argument that the continuum hypothesis is false.
Woodin's Ω-conjecture asserts that if there is a proper class of Woodin cardinals (for technical reasons, most results in the theory are most easily stated under this assumption), then Ω-logic satisfies an analogue of the completeness theorem. From this conjecture, it can be shown that, if there is any single axiom which is comprehensive over (in Ω-logic), it must imply that the continuum is not 
. Woodin also isolated a specific axiom, a variation of Martin's maximum, which states that any Ω-consistent 
(over ) sentence is true; this axiom implies that the continuum is 
.
Logic (disambiguation)
Logic may refer to:
- Mathematical logic, a branch of mathematics that grew out of symbolic logic
- Philosophical logic, the application of formal logic to philosophical problems
Logic may also refer to:
Entertainment
Science and technology
Podcasts:
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by Lojique
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by Logic
Truth Decay
by: LojiqueYou know how some cats want you to think they're holy but they're hellish
They relish every opportunity they have to embellish
The facts, say one thing in your face another behind your back
But I ain't goin out like that
I'm leavin no stone unturned as I burn down your village and maraud
In vain you invoked the name of God but your theory was flawed
I don't wanna hear it Jezebel spirit you tried enticin me
But the Christ in me rises up with wrath righteously
You tried to turn the Page and felt the rage
Warfare is waged as we engaged, feel the fury uncaged
You can't lobotomize me or sodomize me
Get me drunk off your hundred and eighty-proof ninety-percent truth
Ten percent lie you were sent by
Lord of the flies, but angel of light is the alias he went by
It's plain and simple I'm drivin the money changers from the temple
And all the sheisty moves that I've seen them pull
God is comin back wroth with the slack sloth
Imagine your crew geared up in ashes and sackcloth
You're straight from hell, you dispel your own truth
Changing up like Clark Kent in a phone booth
But where's my real ones that do not love their lives unto death
I got a blade to your gut and I'm gonna make you say "Shibboleth"
The surface is an immaculate manicured plot
While the truth lies forgot under the dirt to rot
[Othello, Page One, Braille, Ohmega Watts]
Decayed truth spoken, every tooth broken
From out of the mouth of madness
Destroying your blasphemous tactics shattering your tablets
This is an act of correcting
[repeat]
[Braille]
Activate my mic with electric shockwaves
Wake you up from your sweet dreams
Many speaking filthy lies
Sounding intelligent but I'm not impressed or confused
My short fuse is lit who is this
Braille spittin truth to influence you to quit
Your day job stay off the microphone
If God ain't pleased with your words then leave it alone
[Othello]
Let me start off by stating while the world's fading yo I'm creating
Promptly grab the mic to execute my mission statement
Basic but basically capable of changing and rearranging the art
Of making music from the heart I spark
With Christ-inspired thoughts and pray never to be a has been
So intricate that in sifting it you come up with mad gems
The sin of men and women who pretend to have it all
Together lie in your face and together they will fall
Emcees with truth decay the worst display of halitosis
Wacktose intolerant I'm bothered by the most if
Not all the pseudo synthetic attempts to creativity this industry endorses
Ignorant lyricists spitting nonsense
Lost in space time relevance elements
Raped, battered and bruised, shoved to the bottom of the sea like sediment
Twenty thousand leagues beneath
Underground preserved from insulated heat designated beat
Downs with unique sounds on crews that represent weak so to speak
With leaps and bounds around the middle my pedestal
Splits in two unfortunate but true