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antilogical
antilogical adj. 
/ˌænˌtaɪˈlɑdʒək(ə)l/, /ˌæn(t)əˈlɑdʒək(ə)l/
Brit. /ˌantɪˈlɒdʒᵻkl/
, /ˌantɪˈlɒdʒᵻkl/U.S. /ˌæn(t)iˈlɑdʒək(ə)l/
, /ˌæn(t)iˈlɑdʒək(ə)l//ˌænˌtaɪˈlɑdʒək(ə)l//ˌæn(t)əˈlɑdʒək(ə)l/ΚΠ
1657 M. Nedham Great Accuser cast Down 27 Those sophisticated Suppositions, and those illogical, antilogical Rodomontadoes and hard words.
1701 J. Norris Ess. Ideal World I. vi. 360 There is no great Reason to fear that so Anti-logical a Principle, as that of the Positivity of Truth, will ever come to be the Doctrin of any intire School or University.
1814 S. T. Coleridge Marginalia (1998) IV. 172 Makes for produces, a Gallo-barbarism not less anti-logical than anti-Anglican.
1900 J. Jastrow Fact & Fable in Psychol. 167 The strongly rooted, anti-logical tendencies of our nature..come to the surface in various and unexpected ways.
1997 K. Conboy et al. Writing on Body 10 Woman's sexuality can be translated into a language which might seem to operate in a nonlinear, antilogical way.
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