Full Idea
Connectionist networks have difficulty with the kind/individual distinction (ducks/this duck), with compositionality (relations), with quantification (reference of 'all'), with recursion (embedded thoughts), and the categorical reasoning (exceptions).
Gist of Idea
There are five types of reasoning that seem beyond connectionist systems
Source
report of Steven Pinker (The Blank Slate [2002], Ch.5) by PG - Db (ideas)
Book Reference
Pinker,Steven: 'The Blank Slate' [Penguin 2003], p.80
A Reaction
[Read Pinker p.80!] These are essentially all the more sophisticated aspects of logical reasoning that Pinker can think of. Personally I would be reluctant to say a priori that connectionism couldn't cope with these things, just because they seem tough.