Category Archives: Logic

The Incompatible Properties Argument(s) by T.M. Drange

[This article was originally published by Dr. Theodore Drange in Philo 1998 (2), pp. 49-60. It has been re-purposed here, eliminating most of Drange’s accompanying comments to anticipated objections. The intention here is just to provide the outlines of his argument(s) in their logical form(s) and promote awareness of the argument’s overall strength.]

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Atheological arguments (arguments for the nonexistence of God) can be divided into two main groups. One group consists of arguments which aim to show an incompatibility between two of God’s properties. Let us call those “incompatible-properties arguments.” The other group consists of arguments which aim to show an incompatibility between God’s existence and the nature of the world. They may be called “God-vs.-world arguments.” A prime example of one of those would be the Evidential Argument from Evil. This paper will only survey arguments in the first group. Arguments in the second group are discussed elsewhere.[1]

To generate incompatible-properties arguments, it would be most helpful to have a list of divine attributes. I suggest the following. God is:

(a) perfect                       (g) personal

(b) immutable                (h) free

(c) transcendent            (i) all-loving

(d) nonphysical              (j) all-just

(e) omniscient                (k) all-merciful

(f) omnipresent              (l) the creator of the universe

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Sentential Logic Practice: Assessing Some Proofs

1.) A&B, B > (D&E), derive B > E
(A&B)
B
(D&E)
E
B > E

2.) S > (Q&R), S, derive R
S
(Q&R)
R

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Sentential Logic Practice: Symbolizing Natural Sentences

1.) Natural sentence: Either Joe Biden or Bernie Sanders will get the Democratic Presidential Nomination.
Library: B = Biden will get the Democratic Presidential Nomination
S = Sanders will get the Democratic Presidential Nomination
Symbolization: B∥S

2.) Natural sentence: If you take proper precautions, then you can help slow the spread of the novel coronavirus.
Library: T = you take proper precautions
S = you can help slow the spread of the novel coronavirus

Symbolization: T→S

3.) Natural sentence: Eat your vegetables and your meat before you have dessert.
Library: V = eat your vegetables
M = eat your meat
D = you have dessert

Symbolization: (V&M)→D; (V&M)≡D*
*material bi-conditional/material equivalence, stronger logical symbolization of the statement

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