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Answer for the clue "Illogicality as a consequence of having a conclusion that does not follow from the premisses ", 10 letters:
invalidity

Word definitions for invalidity in dictionaries

Douglas Harper's Etymology Dictionary Word definitions in Douglas Harper's Etymology Dictionary
1540s, from Latin invalidatus (see invalid (adj.)).

WordNet Word definitions in WordNet
n. illogicality as a consequence of having a conclusion that does not follow from the premisses [syn: invalidness ]

Longman Dictionary of Contemporary English Word definitions in Longman Dictionary of Contemporary English
noun COLLOCATIONS FROM CORPUS ■ NOUN benefit ▪ If they remain chronically incapacitated for work they can now claim invalidity benefit at a higher rate. ▪ These are child benefits , industrial injuries and death benefits, certain invalidity benefits, and ...

The Collaborative International Dictionary Word definitions in The Collaborative International Dictionary
Invalidity \In`va*lid"i*ty\, n. [Cf. F. invalidit['e], LL. invaliditas lack of health.] Lack of validity or cogency; lack of legal force or efficacy; invalidness; as, the invalidity of an agreement or of a will. Lack of health; infirmity. [Obs.] --Sir ...

Wiktionary Word definitions in Wiktionary
n. The state of being invalid; lack of validity.

Usage examples of invalidity.

Justice Stone seems to be engaged in an endeavor to erect this into an almost exclusive test of the validity, or invalidity of State taxation affecting interstate commerce.

The laws of both Austra and Nordla derive originally from the Code of Cyad, such of it as remained, and largely from the ensuing case histories, by precedent, and as amended by any proclamations of the lord, provided that the lord justicer does not issue an opinion suggesting the legal invalidity of such a proclamation .

The invalidity or unenforceability of any provision of this agreement shall not void the remaining provisions.

In the one, the maxim in pari delicto potior est [149] conditio defendentis, and the invalidity of contracts contemplating it, show that the conduct is outside the protection of the law.

For all these concepts, nay, all the questions which pure reason places before us, have their origin, not in experience, but in reason itself, and must therefore be capable of being solved and tested as to their validity or invalidity.