Final answer:
The spinal syndrome described is a hemisection of the spinal cord, or Brown-Séquard syndrome, causing loss of pain and temperature sensation on the opposite side of the injury, and motor paralysis and proprioception loss on the same side as the injury.
Step-by-step explanation:
The spinal syndrome in question, characterized by the loss of pain and temperature sensation on one side and motor paralysis and proprioception on the other, is known as hemisection of the spinal cord, or Brown-Séquard syndrome. This condition is caused by damage to one half of the spinal cord, which results in a disruption of the nerve pathways. Specifically, in the case of hemisection, paralysis and loss of proprioception occur on the same side as the injury because the dorsal column pathway and the lateral corticospinal tract, which carry these signals, ascend ipsilaterally. Conversely, the spinothalamic pathway, which carries pain and temperature sensations, decussates at the level of entry into the spinal cord and ascends contralaterally, therefore bypassing the site of hemisection on the injured side and causing a loss of these sensations on the opposite side of the body.