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Interlinked Dictionary© based on 
Merriam-Webster's Collegiate® Dictionary (m-w.com)
and Star Dictionary
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not observing the principles of logic; devoid of logic; senseless, such as this statement by Frederick Turner."The brain is hungry not for method but for content, especially content which contains generalizations that are powerful, precise and explicit.".and note the circular reasoning here
illogicality, illogicalness.nouns

the state of being insolent; despitefulness; arrogance; impudence

if you say that someone is being insolent, you mean they are being rude to someone they ought to be respectful to; disrespectful of custom, methods or caring and helpful opinions and motives of others (decisions against proper and careful safety regulations evidence a rejectionist.motivated by either lack of concern or greed); impudent; arrogant

belonging to the essential nature or constitution of a thing (the intrinsic worth of a gem) (the intrinsic brightness of a star); contrast extrinsic

a speech form or an expression of a given language that is peculiar to itself grammatically or cannot be understood from the individual meanings of its elements, as in 'take to heart', 'in spite of', 'by virtue of', etc.; the language peculiar to a people or to a district, community or class; dialect; the syntactical, grammatical, or structural form peculiar to a language; manner, style

idiomatic means a speech form or an expression of a given language that is peculiar to itself grammatically or cannot be understood from the individual meanings of its elements, as in 'keep tabs on'; of, relating to or conforming to idiom;-peculiar to a particular group, individual or style

imbue, imbued, imbuing, imbues.transitive verbs
to permeate or influence as if by dyeing; to tinge or dye deeply 

extremely slight, gradual or subtle; not perceptible by the senses or mind

imply, implied, implying, implies.transitive verbs
to hint; to indicate without saying openly or directly (his tone implied disapproval; although he didn't directly say it, he implied he would be soon moving into the country); suggest; to involve by logical necessity; entail (life implies learning and growth; to express or indicate.indirectly)

implication.noun, plural.implications
the act of implicating or the condition of being implicated; the act of implying or the condition of being implied; something that is implied, especially (an indirect.indication; a suggestion); an implied.meaning; implicit.significance; suggest; an inference
implicate, implicated, implicating, implicates.transitive verbs
from Latin, to entwine.(to involve, to employ; intimately connected (what is the far reaching implication of his decision?); to implicate someone means to show or claim that they were involved in something having negative effect upon others; to have as a consequence, corollary or natural inference; to imply; to bring into intimate or incriminating connection; to involve in the nature or operation of something; entail (life implies growth through learning)l to involve or connect intimately or incriminatingly (evidence that implicates others in the plot); to have as a consequence or an inference; imply; to interweave or entangle

inculcate, inculcated, inculcating, inculcates, inculcated, inculcating.transitive verbs
to teach and impress upon the mind; to fix ideas, principles etc in someone's mind (she takes efforts to inculcate a sense of responsibility in her children; not all schools manage to successfully inculcate a love of learning); to make part of one's personality makeup by resolve, frequent.contemplation, instruction or repetition; instil; implant; indoctrinate; propagandize
inculcation, inculcator-nouns

devoid of qualities that make for spirit and character.(the new chilies are missing the fire we enjoyed earlier); lacking taste or savor; tasteless; lacking in qualities that interest, stimulate or challenge; dull, flat, boring, unintelligent, selfishly minded
synonyms.vapid, flat, jejune, banal, inane
insipid implies a lack of sufficient taste or savor to please or interest (an insipid romance) 
vapid suggests a lack of liveliness, force or spirit (an exciting story given a vapid treatment)
flat applies to things that have lost their sparkle or zest (although well regarded in its day, the novel now seems flat)

inane, inaner, inanest.adjective
lacking.significance, meaning or point; silly; lacking sense or substance; empty (an inane comment; a ditzy person); implies a lack of any significant or convincing.quality (an inane interpretation of the play); unintelligent-

traveling from place to place, especially to perform work or a duty (an itinerant judge, itinerant labor)
one who travels from place to place

unsure of how to act or proceed; undecided; lacking in resolution; indecisive
irresoluteness or irresolution.nouns

institutionalize, institutionalized, institutionalizing, institutionalizes.transitive verbs
to make part of a structured and usually well established system; to make into, treat as or give the character of an institution to; to place (a person) in the care of an institution

institute, instituted, instituting, institutes.transitive verbs
to establish, organize and set in operation; to initiate; begin institute.noun
something instituted; an organization founded to promote a cause (a research institute); an educational institution, especially one for the instruction of technical subjects; the building or buildings housing such an institution

buildings housing organizations of specialized efforts (a learning institution; a research institution); the act of instituting; customs, practices, relationships or behavioral patterns of importance in the life of a community or society (the institutions of Thanksgiving Day and the family); one long associated with a specified place, position or function; a place for the care of persons who are destitute, disabled or mentally ill

impact, impacted, impacting, impacts.verbs
transitive verb use.to have an effect or impact on; to pack firmly together; wedged or packed in, so as to fill or block an organ or a passage (impacted feces); to strike forcefully (meteorites impacting the lunar surface)
intransitive verb use.to have an effect or impact
the power of making a strong, immediate impression (a speech that lacked impact); the effect or impression of one thing on another (still gauging the impact of automation on the lives of factory workers); the striking of one body against another; collision; the force or impetus transmitted by a collision

difficult to believe; not plausible; if you describe something as implausible, you believe that it is unlikely to be true (I had to admit it sounded like an implausible excuse; it's not entirely implausible that a galaxy could be similar to our own)

if you say that someone has an inalienable right to something, you are emphasizing that they have a right to it which cannot be changed or taken awaythat cannot be transferred to another or others (inalienable or unalienable rights)

the ability to learn and reason; the capacity for knowledge and understanding; the ability to think abstractly or profoundly; mind; a person of great intellectual ability; intelligent

lacking importance; not following from premises or evidence; illogical
a triviality

of no importance or relevance; inconsequential or irrelevant; having no material body or form

lacking substance or reality; immaterial; not firm or solid; flimsy; delicate; fine

incorrupt, incorruptible.adjectives
not subject to corruption or decay; incapable of being morally corrupted
the quality or state of being free from physical decay; characterized by integrity or probity

intersect, intersected, intersecting, intersects.verbs
transitive verb use.to cut across or through (the path intersects the park); to form an intersection with; cross (the road intersects the highway a mile from here)
intransitive verb use.to cut across or overlap each other (circles intersecting on a graph); to form an intersection; cross (these two fences intersect at the creek)
the act, process.or.result of intersecting; a place where things intersect, especially a place where two or more roads cross; in mathematics, the point or locus of points where one line, surface, or solid crosses another; a set that contains elements shared by two or more given sets

a narrow strip of land connecting two larger masses of land

not efficient, as lacking the ability or skill to perform effectively; incompetent (an inefficient manager); not producing the intended result; ineffective (an inefficient campaign against illegal drugs); wasteful of time, energy or materials (an inefficient design; outdated and inefficient methods)

inefficiency.noun, plural.inefficiencies
the quality, condition or fact of being inefficient; an inefficient act, design or procedure (pointed out certain inefficiencies in the many government and corporate concerns)