"deduction" is a synonym of "syllogism". "induction" is an antonym of "deduction"

I was wondering if there is a antonym of "syllogism" which share the same suffix as "syllogism"?

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    A syllogism is a type of deduction, the two words are not synonyms, and induction is not an antonym for either. In fact, you can even use the syllogism form in an inductive argument. The question, as asked, is based on incorrect assumptions. – Chris Sunami supports Monica Oct 31 '13 at 17:59
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    That definition of induction and deduction is well-known, but it doesn't match the current usage, please see here: iep.utm.edu/ded-ind . Since there are technical terms, it's probably best to stick with the technical definitions. Sorry if this seems pedantic --I used to teach logic. – Chris Sunami supports Monica Oct 31 '13 at 18:14
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    @ChrisSunami: what else besides syllogism belong to deduction? – Tim Oct 31 '13 at 19:06
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    Logical terms are being mixed with etymology and great abandon here. Don't forget that synonym and antonym are logical terms, too. +1 for suggesting a -logism libfix, although I'm not sure philosophy is ready for that yet. – John Lawler Oct 31 '13 at 19:37
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    A syllogism is not abstract like deduction, but rather one of a set of fixed linguistic forms for stating logical deductions. Medieval logicians recognized twenty-four (out of 256) modes of the syllogism as being valid, and even gave them mnemonic names. Barbara, Celarent, Darii, Ferio, Barbarix, Feraxo; Cesare, Festino, Camestres, Baroco, Camestrop, Cesarox; etc.). All of them have different kinds of "antonyms", depending. – John Lawler Oct 31 '13 at 19:58

Lewis Carroll provides the answer in ‘Sylvie and Bruno’:

For a complete logical argument, we need two prim Misses –

And they produce – A delusion.

But what is the whole argument called?

A Sillygism.

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    I was asking for a synonym of induction. – Tim Oct 31 '13 at 17:35
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    I can't really upvote this answer but you get a mental +1 from me for the Syvie and Bruno reference! – Chris Sunami supports Monica Oct 31 '13 at 17:51
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    @Tim. Oh yeh, but I couldn' resist. – Barrie England Oct 31 '13 at 18:30

"Sophism" would be the antonym, which the OED defines as:

A specious but fallacious argument, either used deliberately in order to deceive or mislead, or employed as a means of displaying ingenuity in reasoning.

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