From the OED:
1811 R. HOOPER Lexicon Medicum 596/1 Paralogia, a delirium in which the patient talks wildly. 1857 R. G. MAYNE Expos. Lex. Med. Sci. (1860) 877/1 Paralogia,..term for a slight degree of madness or of delirium. 1900 GOULD Dict. Med. (ed. 5) 973/1 Paralogia, difficulty in thinking logically. 1905 S. PATON Psychiatry xiv. 383 Another important symptom [of dementia præcox]..is the grotesque irrelevancy exhibited in replying to questions (Paralogia). 1919 R. M. BARCLAY tr. Kraepelin's Dementia Praecox & Paraphrenia ii. 21 Evasion or paralogia consists in this, that the idea which is next in the chain of thought is suppressed and replaced by another which is related to it. 1923 STEDMAN Med. Dict. (ed. 7) 737/1 Paralogia, false reasoning, involving self-deception. 1965 New Scientist 25 Nov. 605/1 The disorders of generalization are..subdivided into lowering of the level of generalization and distortion of generalization. The..latter seems to be the same as Kleist's ‘paralogia’ and Cameron's ‘overinclusion’.
In one of his essays, Harlan Ellison defines paralogia with an excerpt from a trial, which I paraphrase here:
PROSECUTING ATTY: So then you knocked the victim to the ground?
DEFENDANT: Yes, sir.
PROS: And you kicked him repeatedly?
DEF: Yes, sir.
PROS: And you kicked him to death?
DEF: No, sir.
DEF: I was wearing tennis shoes, everybody knows you can't hurt someone wearing tennis shoes. They're soft shoes.
Paralogia is most typically the employ of logic to defend a thesis that is profoundly illogical, as supplied above by Mr. Ellison. The term originates from psychiatric practice, and in its most profound form, paralogia is symptomatic of schizophrenia.