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Our sense of touch helps us encounter the richness of our natural world. Across a myriad of contexts and repetitions, we have learned to deploy certain exploratory movements in order to elicit perceptual cues that are salient and efficient. The task of identifying optimal exploration strategies and somatosensory cues that underlie our softness perception remains relevant and incomplete. Leveraging psychophysical evaluations combined with computational finite element modeling of skin contact mechanics, we investigate an illusion phenomenon in exploring softness; where small-compliant and large-stiff spheres are indiscriminable. By modulating contact interactions at the finger pad, we find this elasticity-curvature illusion is observable in passive touch, when the finger is constrained to be stationary and only cutaneous responses from mechanosensitive afferents are perceptible. However, these spheres become readily discriminable when explored volitionally with musculoskeletal proprioception available. We subsequently exploit this phenomenon to dissociate relative contributions from cutaneous and proprioceptive signals in encoding our percept of material softness. Our findings shed light on how we volitionally explore soft objects, i.e., by controlling surface contact force to optimally elicit and integrate proprioceptive inputs amidst indiscriminable cutaneous contact cues. Moreover, in passive touch, e.g., for touch-enabled displays grounded to the finger, we find those spheres are discriminable when rates of change in cutaneous contact are varied between the stimuli, to supplant proprioceptive feedback.