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    Popular Lectures on Logic
    Popular Lectures on Logic
    Popular Lectures on Logic
    Ebook103 pages1 hour

    Popular Lectures on Logic

    By John-Michael Kuczynski

    ()

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    About this ebook

    Crisp, easy-to-understand lectures on logic.

    Table of contents:

    30 Principles of Logic
    Mathematical Logic
    Trilingual Logic
    101 Principles of Logic
    Different kinds of Mathematical Functions: A Dialogue
    Fucntions, Bijections and Mapping-relations
    Logic and Formal Truth
    Relations and Ordinal Numbers
    Nine Kinds of Number
    Causality
    Analyticity
    Is Mind an Emergent Property?
    Is Time-travel Possible?
    What is a Formal Language?
    Logic and Inference

    LanguageEnglish
    PublisherJohn-Michael Kuczynski
    Release dateDec 21, 2019
    ISBN9781393371373
    Popular Lectures on Logic
    Author

    John-Michael Kuczynski

    J.-M. Kuczynski, PhD University of California, Professor (philosophy, mathematics, economics) at Bard, SBCC, and VCU. Award-winning author turned cyber-preneur. In Who's Who in the World since 2002. 1-800-969-6596 to get started right away.

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      Book preview

      Popular Lectures on Logic - John-Michael Kuczynski

      30 Principles of Logic

      Excluded Middle

      p or not p

      Either Jim has two cars or Jim does not have two cars. Non-contradiction

      Not both p and not p

      Jim does not both have and not have two cars. Modus Ponens

      If p, and if p entails q, then q.

      If Jim has two cars, and if Jim’s being happy follows from his having two cars, then Jim is happy

      Note: To say that p entails q is to say that q follows from p. Modus Tollens

      If not q, and if p entails q, then not-p.

      If Jim is unhappy, and if Jim’s being happy follows from his having two cars, then Jim does not have two cars

      Contraposition

      p entails q is equivalent with not q entails not p.

      For x is a raven to entail that x is black is for x is non-black to entail that x is a non-raven.

      Double Negation

      p if, and only if, not not p.

      Any given statement is equivalent with the negation of its own negation. Jim has two cars if, and only if, Jim does not not have two cars.

      Note: to say that two statements are equivalent is to say that each entails the other.

      Simplification

      If p and q, then p.

      If Jim has two cars and bill is over 7 ft tall, then jim has two cars Logical Addition

      If p, then either p or q.

      If Jim has two cars, then either Jim has two cars or Bill is over 7 ft tall Additive Identity

      If p, then either p or p.

      If Jim has two cars, then either Jim has two cars or Jim has two cars Multiplicative identity

      If p, then p and p.

      If Jim has two cars, then Jim has two cars and Jim has two cars Transitivity

      If p entails q and q entails r, then p entails r.

      p: Jim has exactly two cars

      q: Jim has an even prime number of cars. r: Jim has a prime number of cars.

      p entails q. q entails r. p entails r.

      Self-equivalence

      p if, and only if, p.

      Any given statement is equivalent with itself.

      Contraction

      p or not-p follows from q.

      No statement does not entail a tautology. Expansion

      If p entails both q and not q, then p is false.

      x is a four-sided triangle entails x has and does not have more than three sides. Therefore, it is false that x is a three-sided triangle

      This law is a consequence of the Law of Non-contradiction, taken in conjunction with modus tollens. it is therefore a derived law

      Generalized Expansion

      If q is a law of logic and p entails not-q, then p is false.

      Explanation: If q is a truth of logic, then q holds in all possible worlds. Therefore, not-q is false in all possible worlds. Therefore, by modus tollens, anything that entails q is false in all possible worlds.

      ––––––––

      Consistency

      If p entails not-p, then not-p.

      No truth is inconsistent with itself.

      p: x is a round square

      q: x has exactly three sides.

      p entails q.

      p also entails not-q.

      Therefore, p entails both q and not-q.

      Given the law of non-contradiction, q and not-q is false. Therefore, by modus tollens, p is false.

      Boolean Modus Ponens

      If all f’s are g’s, then if x is an f, x is also a g.

      This law is an analogue of modus ponens. what modus ponens says about statements, this law says about classes.

      Boolean Modus Tollens

      If all f’s are g’s, then if x is a non-g, x is a non-f

      This law is an analogue of modus tollens. what modus tollens says about statements, this law says about classes.

      Identity of Indiscernibles

      Objects are identical when the same.

      If there is no characteristic that x has that y does not have and no characteristic that y has that x does not have, then x=y

      Indiscernibility of Identicals

      Objects are the same when identical.

      If x and y are the very same object, then there is no characteristic x has that y does not have and no characteristic that y has that x does not have.

      Actuality of Necessity

      What is necessary is actual.

      In other words, if p must be true, then p is true.

      Squares must have four sides; therefore, squares do have four sides.

      Explanation: p is necessarily true if p is true in all possible worlds. if p is true in all possible worlds, then p is true in this world.

      Possibility of Actuality

      What is actual is possible

      In other words, if p is true, then p can be true.

      This law follows from the previous two. Duality (Version 1)

      If p is necessarily true, then not-p is necessarily false.

      Squares have four sides is necessarily true. Therefore, squares do not have four sides is necessarily false.

      Duality (Version 2)

      If p is possible, then p is not necessarily false.

      Jim has two cars is possible. Therefore, Jim has two cars is not necessarily false.

      S5

      If p is unconditionally true, then it is unconditionally the case that p is unconditionally true. Given that squares have four sides is unconditionally true, it follows that squares have four sides is unconditionally true is unconditionally true.

      Distributivity of Necessity

      If p is necessarily true and q is necessarily true, then p and q is necessarily true.

      p: Squares have four sides q: Triangles have three sides

      p is necessarily true, and so is q. Therefore, it is necessarily the case that both p and q. Non-distributivity of Possibility

      Given only that p is possible and that q is possible, it does not follow that they are jointly possible.

      In other words, p and q is possible does not follow from p is possible and q is possible

      p: Jim has more than two cars q: Jim has less than two cars.

      p and q is not possible, even though p is possible and q is possible. Extrusion

      If q is a contradiction, then p or q is equivalent with p.

      Either Jim is wealthy or Squares have three sides is equivalent with Jim is wealthy.

      Absorption

      If q is a tautology, then p and q is equivalent with p.

      Jim is wealthy and Squares have four sides is equivalent with Jim is wealthy. Promiscuity of Necessity

      If p is necessary, then q entails p, for any q.

      Given that squares have four sides is necessary, there is no truth and no falsehood that does not entail it.

      Explanation: If p is necessary, there is no world where not-p is true and a fortiori no world where

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