alogically

a·log·i·cal

(ā-lŏj′ĭ-kəl)
adj.
Beyond or outside the bounds of logic.
a·log′i·cal·ly adv.
a·log′i·cal·ness n.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

alogically

(əˈlɒdʒɪkəlɪ; eɪˈlɒdʒɪkəlɪ)
adv
in an alogical manner
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive ?
We see that she is directing her audience to "mark" (that is, to note or interpret) asemantically or alogically (with "no words").
Nonsense and Rebellion
ALOGICALLY, math-ematically and physiologically middle age begins at 25 and ends at 50.
Is saucy underwear the thong for our love life?; Dr VERNON'S CASEBOOK