Former South Australian government minister Bernard Finnigan has argued his prosecution for child pornography offences must fail on two grounds, and charges should be thrown out.

Finnigan is facing five aggravated counts of attempting to gain access to child pornography and one aggravated charge of obtaining access to child pornography.

He was committed to stand trial in the Adelaide District Court but, after an appeal by Finnigan's lawyers, the Supreme Court overturned the committal order and sent the case back to the Magistrates Court.

Finnigan's lawyer Michael Abbott told the Magistrates Court the prosecution could not prove the children depicted in the pornography were under 14 when the images were produced.

He argued it could not be proved the search terms Finnigan allegedly used would have led him to child pornography.

"The prosecution case must fail because it seeks to infer the actual age (of the children depicted in the images) from the apparent age," he told the hearing.

"[The prosecution] cannot prove that the entry of the search terms that constitute each offence would have led to any child pornography, let alone any that depicted children under the age of 14."

"There is no evidence of what was found by the defendant, if anything, as a result of entering those search terms, of what Google had displayed to the viewer upon entering those search terms."

Mr Abbott said that, because the charge was aggravated, the prosecution had to prove the actual age but he said "one can utilise the apparent age to come to a conclusion on the [non-aggravated] charge".

"The prosecution is now relying on what could have been, or might have been, found. The prosecution alleged that child pornography can be obtained in 2013 using those search terms and asks the court to infer that in 2010 child pornography could have been obtained using those same search words," he argued.

Magistrate Simon Smart said the case raised complex issues.

"Not only are [websites] created but they are also deleted [frequently] so I don't know how you prove what was on the internet in 2010," he said.

Finnigan remains a member of the Legislative Council but is no longer in the ALP.