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The compliant nature of soft fingers allows for safe and dexterous manipulation of objects by humans in an unstructured environment. A soft prosthetic finger design with tactile sensing capabilities for texture discrimination and subsequent sensory stimulation has the potential to create a more natural experience for an amputee. In this work, a pneumatically actuated soft biomimetic finger is integrated with a textile neuromorphic tactile sensor array for a texture discrimination task. The tactile sensor outputs were converted into neuromorphic spike trains, which emulate the firing pattern of biological mechanoreceptors. Spike-based features from each taxel compressed the information and were then used as inputs for the support vector machine classifier to differentiate the textures. Our soft biomimetic finger with neuromorphic encoding was able to achieve an average overall classification accuracy of 99.57% over 16 independent parameters when tested on 13 standardized textured surfaces. The 16 parameters were the combination of 4 angles of flexion of the soft finger and 4 speeds of palpation. To aid in the perception of more natural objects and their manipulation, subjects were provided with transcutaneous electrical nerve stimulation to convey a subset of four textures with varied textural information. Three able-bodied subjects successfully distinguished two or three textures with the applied stimuli. This work paves the way for a more human-like prosthesis through a soft biomimetic finger with texture discrimination capabilities using neuromorphic techniques that provide sensory feedback; furthermore, texture feedback has the potential to enhance user experience when interacting with their surroundings.