How do Catholics support transubstantiation?

As I understand it, the doctrine of transubstantiation maintains that bread and wine *literally*\* become the body and blood of Christ... yet it is impossible to detect this. That is, they do not materially change, so we don't and can't notice, nor can we scientifically show any change. I'm curious: how do Catholics support this view? Especially considering Jesus' statements that the bread and wine were His body and blood could easily be taken as symbolic. --- *In the literal sense of "literally".