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 H_{\aleph_2}. Just as the axiom of projective determinacy yields a canonical theory of H_{\aleph_1}, 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 H_{\aleph_2} (in Ω-logic), it must imply that the continuum is not \aleph_1. Woodin also isolated a specific axiom, a variation of Martin's maximum, which states that any Ω-consistent \Pi_2 (over H_{\aleph_2}) sentence is true; this axiom implies that the continuum is \aleph_2.

Logic (disambiguation)

Logic may refer to:

  • Logic, the study of the principles and criteria of valid inference and demonstration
  • 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

  • "A Logic Named Joe", a science fiction short story by Murray Leinster (using his given name, Will F. Jenkins) first published in the March 1946 issue of Astounding Science Fiction
  • Lamont "LOGiC" Coleman, a musician who collaborated on rapper Jim Jones' fifth studio album, Capo (album) (2011) on E1 Music
  • Logic (rapper), a Maryland rapper
  • Science and technology

  • Digital logic, a class of digital circuits characterized by the technology underlying its logic gates
  • LOGIC (electronic cigarette), an electronic cigarette owned by Logic Technology Development
  • Podcasts:

    PLAYLIST TIME:

    No Logic

    by: White Hinterland

    There is no logic
    No reason
    No logic at all
    To keep holding on
    To the hope
    You'll turn into
    The man I thought you were
    I can't sit still
    I can't stay in one place too long
    Are you comfortable? Are you comfortable?
    I'm moving along.
    Your voice, though stentorian,
    cannot hide the shadow of a doubt
    Your thoughts may seem golden now
    give them time, time to sort them out
    How do you know the name
    the name of the one you love?
    the name of the one you love?
    what does it feel like?
    can it make a sound?




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