Thursday, November 22, 2018

Basic Logic for Theology

It's commonly agreed that we can't have theologic without logic itself. Theology usually is defined as "the doctrine of God" (something to that effect) or more colloquially as "talking about God" whereas "logic" is "the science/study of correct thinking." Logic studies correct ways of thinking, that is, correct inferences. What do we mean by correct inferences? Here are some examples:

1. Modus Ponens

A) If P, then Q
B) P
C) Therefore, Q

2. Modus Tollens

A) If P, then Q
B) Not Q
C) Therefore, Not P

3) Conjunction

A) P
B) Q
C) Therefore, P and Q

4) Hypothetical Syllogism

A) If P, then Q
B) If Q, then R
C) Therefore, If P, then R

5) Disjunctive Syllogism

A) Either P or Q
B) Not P
C) Therefore, Q
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5 comments:

  1. Duncan8:23 AM

    Like electronics:-

    AND, OR, XOR, NOT, NAND, NOR, and XNOR

    No direct equivalency to Hypothetical Syllogism.

    https://www.stetson.edu/artsci/philosophy/media/logicchapter9font.pdf

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  2. Edgar Foster3:43 PM

    Exactly, Duncan. In fact, a rule of inference known as De Morgan's Laws (aka De Morgan's Theorems) has applications in electronics. You may be familiar with those laws: ~(P & Q) = ~P v ~Q and so forth. Tilde stands for "it is not the case that" and the symbol ranges over what's in the parentheses.

    For the last 2 semesters that I've taught logic, I've used a book written by Richard Arthur entitled An Introduction to Logic. He employs the ampersand (&) to signify "and" or conjunction, but he uses the negation bar instead of tilde to indicate negation. We also do truth tables for conjunction, conditionality, negation, biconditionality, and disjunction. We also distinguish between inclusive and exclusive injunction, we learn about quantification theory and more.

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  3. Edgar Foster3:45 PM

    I also like transposition: If P, then Q = If not Q, then not P.

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  4. Duncan1:22 AM

    http://hyperphysics.phy-astr.gsu.edu/hbase/Electronic/DeMorgan.html

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  5. Edgar Foster9:55 PM

    Lot of information about conditional statements here: https://www.google.com/search?q=if+p%2C+then+not+q&oq=if+p%2C+then+not+q&aqs=chrome..69i57j0l5.4234j0j8&sourceid=chrome&ie=UTF-8

    Example of a conditional statement: "If P, then Q"

    Example of biconditional statement: "P if and only if (IFF) Q"

    Use the one-directional arrow for conditional statements, but the double arrow for biconditional statements.

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