In this paper, a novel tactile sensing mechanism for soft robotic fingers is proposed. Inspired by the proprioception mechanism found in mammals, the proposed approach infers tactile information from a strain sensor attached on the finger's tendon. We perform experiments to test the tactile sensing capabilities of the proposed structures, and our results indicate this method is capable of palpating texture and stiffness in both abduction and flexion contact. Under systematic cross validation, the proposed system achieved 100% and 99.7% accuracy in texture and stiffness discrimination respectively, which validate the viability of this approach. Furthermore, we use statistics tools to determine the significance of various features extracted for classification.