Alkene Electrophilic Addition Reaction Stereoselectivity When Two New Asymmetric Centers Form I had a question about the stereoselectivity in electrophilic addition reactions (specific to alkenes) that form additional asymmetric centers in their products. I understand that when a reactant with one preexisting asymmetric center forms a product with an additional asymmetric center, the two possible product stereoisomers are a pair of diastereomers because the configuration for the preexisting asymmetric center will stay the same while the configuration of the  newly formed asymmetric center will vary. Since diastereomers differ in stability, their transition states differ as well, therefore the product with greater stability will come from a transition state with lower energy, which will require less activation energy to form. The product stereoisomer with greater stability therefore forms faster and becomes the predominant product. 

However, the textbook also says that the electrophilic addition reactions that form products with two additional asymmetric centers from a reactant without any asymmetric center form four stereoisomers of which two pairs are enantiomers with each other.

It is also mentioned that this kind of reaction is not stereoselective. I don't understand how this is the case; the members that form enantiomers with each other might be energetically identical, but the stereoisomers that are diastereomers to each other must be energetically different, thus having different stability. If the logic from the first case applies the same here, wouldn't the reactions that form two new additional asymmetric centers also be stereoselective since they form diastereomers?
Stereoselective becomes a hand-wavy term as soon as you may end up with more than one type of stereoisomer. If you want to actually state what is going on, you would most likely use either of the terms enantioselective (selects for a specific enantiomer) or diastereoselective (selects for a specific diastereomer; this may or may not include both enantiomers of the diastereomer).

In the first case, there is only one selectivity that can be observed; you can only get diastereomers, no enantiomers. Therefore, there may be some reason in shortening the term to stereoselective. In the second case you should not resort to using stereoselective because it is not specific enough — and that is irrelevant of the question whether stereospecificity is observed or not.

The second reaction would likely indeed be diastereoselective to a certain extent while definitely not being enantioselective (because the product is symmetric). So calling it diastereoselective — and thus, by intrapolation, stereoselective — may be justified.

In practice, the selectivities of both reactions would be so low that no practicing organic chemist would call either ‘selective’.