Webster's Revised Unabridged Dictionary · 1913

Inconsequent

Inconsequent , adjective

[Latin inconsequens: compare French inconséquent. See In- not, and Consequent.]

Not following from the premises; not regularly inferred; invalid; not characterized by logical method; illogical; arbitrary; inconsistent; of no consequence.
Loose and inconsequent conjectures. — Sir T. Browne